Curriculum Vitae of MICHAEL RENARDY

Born: April 9, 1955
German, U.S. Resident Alien
Married to Mama Bear, three children: Sister Bear, Brother Bear, Baby Bear

Hobbies
I am an amateur composer. Links to my compositions can be found here.
Education
Schelztor-Gymnasium, Esslingen, Class of 1973
Dipl. Math., Universität Stuttgart, Nov. 1977
Dipl. Phys., Universität Stuttgart, Dec. 1978
Dr. rer. nat., Universität Stuttgart, Feb. 1980
Supported by Studienstiftung des deutschen Volkes 1973-1978
Click here for details of my academic ancestry (some of it goes back to the 11th century). A list of comments on the table can be found here.

Professional Employment
Research Associate, Inst. f. theor. Phys., Universität Stuttgart, Apr. 1978-Aug. 1980
Two-year fellowship by Deutsche Forschungsgemeinschaft:
Math. Research Center, Univ. of Wisconsin, Sep. 1980-Aug. 1981;
Dept. of Aerospace Eng., Univ. of Minnesota, Sep. 1981-Aug. 1982
Van Vleck Assistant Professor, Dept. of Math. and Math. Research Center, Univ. of Wisconsin, Aug. 1982-July 1983
Assistant Professor, Dept. of Math. and Math. Research Center, Univ. of Wisconsin, Aug. 1983-Aug. 1985
Associate Professor, Dept. of Math. and Math. Research Center, Univ. of Wisconsin, Aug. 1985-July 1986
Associate Professor, Dept. of Mathematics, Virginia Polytechnic Institute and State University, Sep. 1986-Aug. 1989
Full Professor, Dept. of Mathematics, Virginia Polytechnic Institute and State University, since Aug. 1989
Class of 1950 Professor, Dept. of Mathematics, Virginia Polytechnic Institute and State University, since Oct. 2000
Visiting Fellow, Centre for Mathematical Analysis, Australian National University, June 1984 and July-Aug. 1988
Visiting Professor, Inst. for Mathematics and its Appl., Univ. of Minnesota, Jan.-June 1989 and Sep.-Dec. 2009
Visiting Professor, Mathematisches Institut A, Universität Stuttgart, May-Aug. 1991
Visiting Professor, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Jan.-June 1996

Fields of Interest
Nonlinear partial differential equations, non-Newtonian fluids, free surface flows, stability and bifurcation

Membership in Professional Societies
Society for Industrial and Applied Mathematics (1981)
Society of Rheology (1982)
American Mathematical Society (1983)
Society for Natural Philosophy (1984)
International Society for the Interaction of Mechanics and Mathematics (1985), Executive Committee Member 2000-2003
American Physical Society, Division of Fluid Dynamics (1997)

Prizes and Awards
Bundessieger, Bundeswettbewerb Mathematik des Stifterverbandes für die deutsche Wissenschaft (1973)
Presidential Young Investigator Award (1985)
Virginia Tech Alumni Award for Research Excellence (1993)

I am an editor of the following journals and book series:
Co-Editor, Z. angew. Math. Phys., 1988-1990
Editor, Z. angew. Math. Phys., since 1991
Co-Editor, SIAM J. Math. Anal., 1993-1999
Co-Editor, Math. Meth. Appl. Sci., since 1994
Co-Editor, Adv. Diff. Eq., 1995-2002
Editor, AMS Mathematical Surveys and Monographs, 1996-1999
Co-Editor, Comm. Appl. Anal., since 1997
Co-Editor, Internat. J. Diff. Eq. Appl., since 1999
Co-Editor, SIAM Electronic Problems and Solutions, since 1999
Co-Editor, Internat. J. Pure Appl. Math., since 2001
Co-Editor, Z. angew. Math. Mech., since 2005
Co-Editor, Qualitative Theory of Differential Equations and Applications, since 2006
Co-Editor, International Journal of Mathematics and Computation, since 2008

Graduate Students
Alfred Kenric Mulzet, PhD 1997
Thomas Hagen, PhD 1998
Tirivanhu Chinyoka, coadvised with Y. Renardy, PhD 2004
Evgeny Savelev, PhD 2009

Publications

A. Books
(with W.J. Hrusa and J.A. Nohel), Mathematical Problems in Viscoelasticity, Pitman Monographs and Surveys in Pure and Applied Mathematics 35, Longman 1987, 273 pp.
(with R.C. Rogers), An Introduction to Partial Differential Equations, Texts in Applied Mathematics 13, Springer 1993, 2004, 434 pp.
Mathematical Analysis of Viscoelastic Flows, CBMS-NSF Conference Series in Applied Mathematics 73, SIAM 2000, 104 pp.

B. Books Edited
(with A.S. Lodge and J.A. Nohel), Viscoelasticity and Rheology, Academic Press 1985

C. Invited Reviews
1. (with W.J. Hrusa and J.A. Nohel), Initial value problems in viscoelasticity, Appl. Mech. Rev. 41 (1988), pp. 371-378
2. Mathematical analysis of viscoelastic flows, Ann. Rev. Fluid Mech. 21 (1989), pp. 21-36
3. (with Y. Renardy), Stability and instability in viscous fluids, in: S. Friedlander and D. Serre (eds.), Handbook of Mathematical Fluid Dynamics 2, Elsevier 2003, pp. 223-287
4. Topics in mathematical analysis of viscoelastic flow, in: D.Y. Gao and R.W. Ogden (eds.), Advances in Mechanics and Mathematics, Vol. 2, Kluwer 2003, pp. 109-143
5. Self-similar breakup of non-Newtonian liquid jets, Rheol. Rev. 2004, pp. 171-196
6. Mathematical analysis of viscoelastic fluids, in: C. Dafermos and M. Pokorny (eds.), Handbook of Differential Equations: Evolutionary Equations 4, Elsevier 2008, pp. 229-265

D. Papers in Scientific Journals
1. Hopf-Bifurkation bei Lasern, Math. Meth. Appl. Sci. 1 (1979), pp. 194-213
2. On bounded solutions of a classical Yang-Mills equation, Comm. Math. Phys. 76 (1980), pp. 277-287
3. Bifurcation from rotating waves, Arch. Rat. Mech. Anal. 79 (1982), pp. 49-84
4. A quasilinear parabolic equation describing the elongation of thin filaments of polymeric liquids, SIAM J. Math. Anal. 13 (1982), pp. 226-238
5. Bifurcation of singular solutions in reversible systems and application to reaction-diffusion equations, Adv. Appl. Math. 3 (1982), pp. 384-406
6. Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids, Rheol. Acta 21 (1982), pp. 251-254
7. (with H. Haken), Bifurcation of solutions of the laser equations, Physica D 8 (1983), pp. 57-89
8. (with P. Markowich), A nonlinear Volterra integrodifferential equation describing the stretching of polymeric liquids, SIAM J. Math. Anal. 14 (1983), pp. 66-97
9. (with P. Markowich), The numerical solution of a class of quasilinear parabolic Volterra equations arising in polymer rheology, SIAM J. Num. Anal. 20 (1983), pp. 890-908
10. A class of quasilinear parabolic equations with infinite delay and application to a problem of viscoelasticity, J. Diff. Eq. 48 (1983), pp. 280-292
11. Local existence theorems for the first and second initial-boundary value problems for a weakly non-Newtonian fluid, Arch. Rat. Mech. Anal. 83 (1983), pp. 229-244
12. Singularly perturbed hyperbolic evolution problems with infinite delay and an application to polymer rheology, SIAM J. Math. Anal. 15 (1984), pp. 333-349
13. (with P. Markowich), Lax-Wendroff methods for hyperbolic history value problems, SIAM J. Num. Anal. 21 (1984), pp. 24-51 (Corrigendum: SIAM J. Num. Anal. 22 (1985), p. 204)
14. On the domain space for constitutive laws in linear viscoelasticity, Arch. Rat. Mech. Anal. 85 (1984), pp. 21-26
15. (with D.D. Joseph and Y. Renardy), Instability of the flow of two immiscible liquids with different viscosities in a pipe, J. Fluid Mech. 141 (1984), pp. 309-317
16. (with M. Ahrens, D.D. Joseph and Y. Renardy), Remarks on the stability of viscometric flow, Rheol. Acta 23 (1984), pp. 345-354
17. A local existence and uniqueness theorem for a K-BKZ fluid, Arch. Rat. Mech. Anal. 88 (1985), pp. 83-94
18. (with P. Markowich), A finite difference study of the stretching and break-up of filaments of polymer solutions, J. Non-Newtonian Fluid Mech. 17 (1985), pp. 13-22
19. (with D.D. Joseph and J.C. Saut), Hyperbolicity and change of type in the flow of viscoelastic fluids, Arch. Rat. Mech. Anal. 87 (1985), pp. 213-251 (reprinted in: B.D. Coleman, M. Feinberg and J. Serrin (eds.), Analysis and Thermomechanics, Springer 1987, pp. 25-63)
20. (with W.J. Hrusa ), On wave propagation in linear viscoelasticity, Quart. Appl. Math. 43 (1985), pp. 237-254
21. Existence of slow steady flows of viscoelastic fluids with differential constitutive equations, Z. angew. Math. Mech. 65 (1985), pp. 449-451
22. (with D.D. Joseph, Y. Renardy and K. Nguyen), Stability of rigid motions and rollers in bicomponent flows of immiscible liquids, J. Fluid Mech. 153 (1985), pp. 151-165
23. (with Y. Renardy), Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids, Phys. Fluids 28 (1985), pp. 2699-2708
24. Appendix: A remark on the nonexistence of multiple states or S-shaped curves in kinetic dumbbell theories, in: X.-J. Fan and R.B. Bird, Configuration-dependent friction coefficients and elastic dumbbell rheology, J. Non-Newtonian Fluid Mech. 18 (1985), pp. 255-272
25. (with D.D. Joseph), Hopf bifurcation in two-component flow, SIAM J. Math. Anal. 17 (1986), pp. 894-910
26. (with W.J. Hrusa ), On a class of quasilinear partial integrodifferential equations with singular kernels, J. Diff. Eq. 64 (1986), pp. 195-220
27. Dense imbedding of test functions in certain function spaces, Trans. Amer. Math. Soc. 298 (1986), pp. 241-243
28. (with K.R. Rajagopal, Y. Renardy and A.S. Wineman), Flow of viscoelastic fluids between plates rotating about distinct axes, Rheol. Acta 25 (1986), pp. 259-267
29. Some remarks on the Navier-Stokes equations with a pressure dependent viscosity, Comm. Part. Diff. Eq. 11 (1986), pp. 779-793
30. (with Y. Renardy), Linear stability of plane Couette flow of an upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech. 22 (1986), pp. 23-33
31. A model equation in combustion theory exhibiting an infinite number of secondary bifurcations, Physica D 28 (1987), pp. 155-167
32. Inflow boundary conditions for steady flows of viscoelastic fluids with differential constitutive laws, Rocky Mt. J. Math. 18 (1988), pp. 445-453 (Corrigendum: Rocky Mt. J. Math. 19 (1989), p. 561)
33. (with W.J. Hrusa ), An existence theorem for the Dirichlet problem in the elastodynamics of incompressible materials, Arch. Rat. Mech. Anal. 102 (1988), pp. 95-117 (Corrigendum: Arch. Rat. Mech. Anal. 110 (1990), pp. 373-375)
34.Existence of slow steady flows of viscoelastic fluids of integral type, Z. angew. Math. Mech. 68 (1988), pp. T40-T44
35. Recent advances in the mathematical theory of steady flow of viscoelastic fluids, J. Non-Newtonian Fluid Mech. 29 (1988), pp. 11-24
36. (with W.J. Hrusa ), A model equation for viscoelasticity with a strongly singular kernel, SIAM J. Math. Anal. 19 (1988), pp. 257-269
37. Coercive estimates and existence of solutions for a model of one-dimensional viscoelasticity with a non-integrable memory function, J. Integral Eq. Appl. 1 (1988), pp. 7-16
38. (with Y. Renardy), Bifurcating solutions at the onset of convection in the Bénard problem for two fluids, Physica D 32 (1988), pp. 227-252
39. (with A. Al-Droubi), Energy methods for a parabolic-hyperbolic interface problem arising in electromagnetism, Z. angew. Math. Phys. 39 (1988), pp. 931-936
40. On Rankine-Hugoniot conditions for Maxwell liquids, J. Non-Newtonian Fluid Mech. 32 (1989), pp. 69-77
41. (with Y. Renardy), Stability of shear flows of viscoelastic fluids under perturbations perpendicular to the plane of flow, J. Non-Newtonian Fluid Mech. 32 (1989), pp. 145-155
42. Existence of steady flows of viscoelastic fluids of Jeffreys type with traction boundary conditions, Diff. Integral Eq. 2 (1989), pp. 431-437
43. (with D.D. Joseph), Stokes' first problem for linear viscoelastic fluids with finite memory, Rheol. Acta 28 (1989), pp. 453-456
44. Local existence of solutions of the Dirichlet initial-boundary value problem for incompressible hypoelastic materials, SIAM J. Math. Anal. 21 (1990), pp. 1369-1385
45. Corner singularities between free surfaces and open boundaries, Z. angew. Math. Phys. 41 (1990), pp. 419-425
46. Short wave instabilities resulting from memory slip, J. Non-Newtonian Fluid Mech. 35 (1990), pp. 73-76
47. An alternative approach to inflow boundary conditions for Maxwell fluids in three space dimensions, J. Non-Newtonian Fluid Mech. 36 (1990), pp. 419-425
48. Compatibility conditions at corners between walls and inflow boundaries for fluids of Maxwell type, Z. angew. Math. Mech. 71 (1991), pp. 37-45
49. (with Y. Renardy), On the nature of boundary conditions for flows with moving free surfaces, J. Comp. Phys. 93 (1991), pp. 325-335
50. An existence theorem for model equations resulting from kinetic theories of polymer solutions, SIAM J. Math. Anal. 22 (1991), pp. 313-327
51. (with D.D. Joseph, J. Nelson and Y. Renardy), Two-dimensional cusped interfaces, J. Fluid Mech. 223 (1991), pp. 383-409
52. Ill-posedness at the boundary for elastic solids sliding under Coulomb friction, J. Elasticity 27 (1992), pp. 281-287
53. (with Y. Renardy), Pattern selection in the Bénard problem for a viscoelastic fluid, Z. angew. Math. Phys. 43 (1992), pp. 154-180
54. An existence theorem for a free surface flow problem with open boundaries, Comm. Part. Diff. Eq. 17 (1992), pp. 1387-1405
55. A rigorous stability proof for plane Couette flow of an upper convected Maxwell fluid at zero Reynolds number, Euro. J. Mech. B 11 (1992), pp. 511-516
56. A centre manifold theorem for hyperbolic PDEs, Proc. Roy. Soc. Edinburgh 122A (1992), pp. 363-377
57. (with D.G. Baird), Report on the VIIth International Workshop on Numerical Methods in Non-Newtonian Flow, J. Non-Newtonian Fluid Mech. 43 (1992), pp. 383-385
58. A possible explanation of "bamboo waves" in core-annular flow of two liquids, Theor. Comp. Fluid Dyn. 4 (1992), pp. 95-99
59. (with R.C. Rogers), Shock conditions for hypoelastic materials, Theor. Comp. Fluid Dyn. 5 (1993), pp. 162-170
60. On the stability of parallel shear flow of an Oldroyd B fluid, Diff. Integral Eq. 6 (1993), pp. 481-489
61. On the type of certain C0-semigroups, Comm. Part. Diff. Eq. 18 (1993), pp. 1299-1307
62. The stresses of an upper convected Maxwell fluid in a Newtonian velocity field near a reentrant corner, J. Non-Newtonian Fluid Mech. 50 (1993), pp. 127-134
63. (with Y. Renardy), Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows, Phys. Fluids A 5 (1993), pp. 2738-2762 (Corrigendum: Phys. Fluids A 6 (1994), p. 3502)
64. (with H. Amann), Reaction-diffusion problems in electrolysis, Nonlinear Diff. Eq. Appl. 1 (1994), pp. 91-117
65. Some comments on the surface-tension driven breakup (or the lack of it) of viscoelastic jets, J. Non-Newtonian Fluid Mech. 51 (1994), pp. 97-107
66. On an eigenvalue problem arising in the study of the stability of ocean currents, Z. angew. Math. Phys. 45 (1994), pp. 497-501
67. How to integrate the upper convected Maxwell (UCM) stresses near a singularity (and maybe elsewhere, too), J. Non-Newtonian Fluid Mech. 52 (1994), pp. 91-95
68. On the linear stability of hyperbolic PDEs and viscoelastic flows, Z. angew. Math. Phys. 45 (1994), pp. 854-865
69. Instability of uniform flow, Int. J. Num. Meth. Fluids 19 (1994), pp. 687-692
70. Existence of steady flows for Maxwell fluids with traction boundary conditions on open boundaries, Z. angew. Math. Mech. 75 (1995), pp. 153-155
71. (with Z. Liu), A note on the equations of a thermoelastic plate, Appl. Math. Lett. 8 (1995), No. 3, pp. 1-6
72. A matched solution for corner flow of the upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech. 58 (1995), pp. 83-89
73. On the mechanism of drag reduction, J. Non-Newtonian Fluid Mech. 59 (1995), pp. 93-101
74. A numerical study of the asymptotic evolution and breakup of Newtonian and viscoelastic jets, J. Non-Newtonian Fluid Mech. 59 (1995), pp. 267-282
75. Polar decomposition of positive operators and a problem of Crandall and Lions, Applic. Anal. 57 (1995), pp. 383-385
76. On the stability of differentiability of semigroups, Semigroup Forum 51 (1995), pp. 343-346
77. Instability proof for some transonic problems with resonant mode crossings, Theor. Comp. Fluid Dyn. 7 (1995), pp. 457-461
78. Nonlinear stability of flows of Jeffreys fluids at low Weissenberg numbers, Arch. Rat. Mech. Anal. 132 (1995), pp. 37-48
79. Hopf bifurcation on the hexagonal lattice with small frequency, Adv. Diff. Eq. 1 (1996), pp. 283-299
80. Singular value decomposition in Minkowski space, Lin. Alg. Appl. 236 (1996), pp. 53-58
81. (with Y. Renardy, R. Sureshkumar and A.N. Beris), Hopf-Hopf and steady-Hopf mode interactions in Taylor-Couette flow of an upper convected Maxwell liquid, J. Non-Newtonian Fluid Mech. 63 (1996), pp. 1-31
82. Initial value problems with inflow boundaries for Maxwell fluids, SIAM J. Math. Anal. 27 (1996), pp. 914-931
83. On an equation describing the spreading of surfactants on thin films, Nonlin. Anal. 26 (1996), pp. 1207-1219
84. A singularly perturbed problem related to surfactant spreading on thin films, Nonlin. Anal. 27 (1996), pp. 287-296
85. Spectrally determined growth is generic, Proc. Amer. Math. Soc. 124 (1996), pp. 2451-2453
86. A degenerate parabolic-hyperbolic system modeling the spreading of surfactants, SIAM J. Math. Anal. 28 (1997), pp. 1048-1063
87. Imposing "no" boundary condition at outflow: Why does it work? Int. J. Num. Meth. Fluids 24 (1997), pp. 413-417
88. Qualitative correlation between viscometric and linear viscoelastic functions, J. Non-Newtonian Fluid Mech. 68 (1997), pp. 133-135
89. High Weissenberg number boundary layers for the upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech. 68 (1997), pp. 125-132
90. Reentrant corner behavior of the PTT fluid, J. Non-Newtonian Fluid Mech. 69 (1997), pp. 99-104
91. The high Weissenberg number limit of the UCM model and the Euler equations, J. Non-Newtonian Fluid Mech. 69 (1997), pp. 293-301
92. (with J. Perkins), Stability of equatorial currents with nonzero potential vorticity, Geophys. Astrophys. Fluid Dyn. 85 (1997), pp. 31-64
93. (with A.V. Coward, Y. Renardy and J.R. Richards), Temporal evolution of periodic disturbances in two-layer Couette flow, J. Comp. Phys. 132 (1997), pp. 346-361
94. (with T. Hagen), Boundary layer analysis of the Phan-Thien Tanner and Giesekus model in high Weissenberg number flow, J. Non-Newtonian Fluid Mech. 73 (1997), pp. 181-189
95. Equilibrium configurations of an inflated cylindrical membrane, J. Elasticity 46 (1997), pp. 255-261
96. (with Y. Renardy), Influence of non-Boussinesq effects on patterns in salt finger convection, Z. angew. Math. Phys. 49 (1998), pp. 224-250
97. (with O. Hassager and M.I. Kolte), Failure and nonfailure of fluid filaments in extension, J. Non-Newtonian Fluid Mech. 76 (1998), pp. 137-151
98. (with Y. Renardy), A model equation for axisymmetric stability of small-gap parallel-plate flows, J. Non-Newtonian Fluid Mech. 77 (1998), pp. 103-114
99. Well-posedness of the shallow water equations in the presence of a front, Diff. Integral Eq. 11 (1998), pp. 95-105
100. (with J. Li and Y. Renardy), A numerical study of periodic disturbances in two-layer Couette flow, Phys. Fluids 10 (1998), pp. 3056-3071
101. (with A.K. Mulzet), Exponential stability for a diffusion equation in polymer kinetic theory, Comm. Appl. Anal. 3 (1999), pp. 305-325
102. (with H.J. Wilson and Y. Renardy), Structure of the spectrum in zero Reynolds number shear flow of the UCM and Oldroyd-B liquids, J. Non-Newtonian Fluid Mech. 80 (1999), pp. 251-268
103. (with Y. Renardy), Instability due to second normal stress jump in two-layer shear flow of the Giesekus fluid, J. Non-Newtonian Fluid Mech. 81 (1999), pp. 215-234
104. A note on bifurcation problems in large containers, Fluid Dyn. Res. 24 (1999), pp. 189-199
105. Bifurcation of traveling waves resulting from resonant mode crossings in oceanic currents, Euro. J. Mech. B 18 (1999), pp. 35-46
106. (with D.L. Russell), Formability of linear elastic structures with volume-type actuation, Arch. Rat. Mech. Anal. 149 (1999), pp. 97-122
107. (with Y. Renardy and K. Fujimura), Takens-Bogdanov bifurcation on the hexagonal lattice for double-layer convection, Physica D 129 (1999), pp. 171-202
108. A boundary value problem for Laplace's equation, Complex Variables 41 (2000), pp. 145-150
109. Boundary layers for Maxwell liquids, Arch. Rat. Mech. Anal. 152 (2000), pp. 93-102
110. (with T. Hagen), Non-adiabatic elongational flow of viscoelastic melts, Z. angew. Math. Phys. 51 (2000), pp. 845-866
111. Asymptotic structure of the stress field in flow past a cylinder at high Weissenberg number, J. Non-Newtonian Fluid Mech. 90 (2000), pp. 23-33
112. Current issues in non-Newtonian flows: a mathematical perspective, J. Non-Newtonian Fluid Mech. 90 (2000), pp. 243-259
113. (with J. Li and Y. Renardy), Numerical simulation of breakup of a viscous drop in simple shear flow with a volume-of-fluid method, Phys. Fluids 12 (2000), pp. 269-282
114. Location of the continuous spectrum in complex flows of the UCM fluid, J. Non-Newtonian Fluid Mech. 94 (2000), pp. 75-85
115. (with T. Hagen), Eigenvalue asymptotics in non-isothermal elongational flow, J. Math. Anal. Appl. 252 (2000), pp. 431-443
116. (with T. Hagen), Studies on the linear equations of melt-spinning of viscous fluids, Diff. Integral Eq. 14 (2001), pp. 19-36
117. Shape control by collinear actuators, Arch. Rat. Mech. Anal. 156 (2001), pp. 231-240
118. Self-similar breakup of a Giesekus jet, J. Non-Newtonian Fluid Mech. 97 (2001), pp. 283-293
119. (with I. Lasiecka and R. Triggiani), Backward uniqueness for thermoelastic plates with rotational forces, Semigroup Forum 62 (2001), pp. 217-242
120. Finite time breakup of viscous filaments, Z. angew. Math. Phys. 52 (2001), pp. 881-887 (Corrigendum: 58 (2007), pp. 904-905)
121. (with Y. Renardy and J. Li ), Numerical simulation of moving contact line problems using a volume-of-fluid method, J. Comp. Phys. 171 (2001), pp. 243-263
122. (with Y. Renardy and V. Cristini), A volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio, Euro. J. Mech. B 21 (2002), pp. 49-59
123. Self-similar jet breakup for a generalized PTT model, J. Non-Newtonian Fluid Mech. 103 (2002), pp. 261-269
124. Higher order Neumann problems for Laplace's equation in two dimensions, Diff. Integral Eq. 15 (2002), pp. 1273-1279
125. Similarity solutions for jet breakup for various models of viscoelastic fluids, J. Non-Newtonian Fluid Mech. 104 (2002), pp. 65-74
126. The effect of upstream boundary conditions on stability of fiber spinning in the highly elastic limit, J. Rheol. 46 (2002), pp. 1023-1028
127. (with D. Losh), Similarity solutions for jet breakup in a Giesekus fluid with inertia, J. Non-Newtonian Fluid Mech. 106 (2002), pp. 17-27
128. (with Y. Renardy), PROST: A Parabolic Reconstruction Of Surface Tension for the volume-of-fluid method, J. Comp. Phys. 183 (2002), pp. 400-421
129. Spectrally determined growth for creeping flow of the upper convected Maxwell fluid, Semigroup Forum 66 (2003), pp. 171-178
130. (with Y. Renardy, S. Popinet, L. Duchemin, S. Zaleski, C. Josserand, M.A. Drumright-Clarke, D. Richard, C. Clanet and D. Quéré), Pyramidal and toroidal water drops after impact on a solid surface, J. Fluid Mech. 484 (2003), pp. 69-83
131. Stress integration for the constitutive law of the upper convected Maxwell fluid near the corners in a driven cavity, J. Non-Newtonian Fluid Mech. 112 (2003), pp. 77-84
132. Parallel shear flows of fluids with a pressure dependent viscosity, J. Non-Newtonian Fluid Mech. 114 (2003), pp. 229-236
133. On damping in two-layer elastic-viscoelastic media, Z. angew. Math. Mech. 84 (2004), pp. 205-210
134. On localized Kelvin-Voigt damping, Z. angew. Math. Mech. 84 (2004), pp. 280-283
135. (with Y. Renardy), Similarity solutions for breakup of jets of power law fluids, J. Non-Newtonian Fluid Mech. 122 (2004), pp. 303-312
136. A comment on self-similar breakup for inertialess Newtonian liquid jets, IMA J. Appl. Math. 70 (2005), pp. 353-358
137. (with P. Wapperom), Numerical prediction of the boundary layers in the flow around a cylinder using a fixed velocity field, J. Non-Newtonian Fluid Mech. 125 (2005), pp. 35-48
138. Post-breakup asymptotics for a Giesekus jet, J. Non-Newtonian Fluid Mech. 126 (2005), pp. 1-5
139. When is a given set of PDEs part of an elliptic system?, Diff. Integral Eq. 18 (2005), pp. 233-239
140. Parallel shear flows of fluids with a temperature dependent viscosity, Z. angew. Math. Phys. 56 (2005), pp. 681-693
141. (with D.B. Khismatullin and Y. Renardy), Development and implementation of VOF-PROST for 3D viscoelastic liquid-liquid simulations, J. Non-Newtonian Fluid Mech. 140 (2006), pp. 120-131
147. A comment on smoothness of viscoelastic stresses, J. Non-Newtonian Fluid Mech. 138 (2006), pp. 204-205
148. Viscoelastic stagnation point flow in a wake, J. Non-Newtonian Fluid Mech. 138 (2006), pp. 206-208
149. On control of shear flow of an upper convected Maxwell fluid, Z. angew. Math. Mech. 87 (2007), pp. 213-218
150. On the use of Laplace transform inversion for reconstruction of relaxation spectra, J. Non-Newtonian Fluid Mech. 154 (2008), pp. 47-51
151. Stability of viscoelastic shear flows in the limit of high Weissenberg and Reynolds numbers, J. Non-Newtonian Fluid Mech. 155 (2008), pp. 124-129
152. (with S. Afkhami, Y. Renardy, J.S. Riffle and T. St. Pierre), Field-induced motion of ferrofluid droplets through immiscible viscous media, J. Fluid Mech. 610 (2008), pp. 363-380
153. Global existence of solutions for shear flow of certain viscoelastic fluids, J. Math. Fluid Mech. 11 (2009), pp. 91-99
154. Some global stability results for shear flows of viscoelastic fluids, J. Math. Fluid Mech. 11 (2009), pp. 100-109
155. Controllability of viscoelastic stresses for nonlinear Maxwell models, J. Non-Newtonian Fluid Mech. 156 (2009), pp. 70-74
156. Ill-posedness of the hydrostatic Euler and Navier-Stokes equations, Arch. Rat. Mech. Anal.
157. Short wave stability for inviscid shear flow, SIAM J. Appl. Math. 69 (2009), pp. 763-768
158. A note on a class of observability problems for PDEs, Syst. Control Lett. 58 (2009), pp. 183-187
159. Stressmodes in linear stability of viscoelastic flows, J. Non-Newtonian Fluid Mech. 159 (2009), pp. 137-140
160. (with Y. Renardy), Linear stability of homogeneous elongational flow of the upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech. 160 (2009), pp. 168-175
161. (with Y. Renardy, S. Assighaou and L. Benyahia), Numerical simulation of drop retraction after a strain jump, Phys. Rev. E 79 (2009) 046323, pp. 1-4
162. On hydrostatic free surface problems, J. Math. Fluid Mech.

E. Submitted for Publication
1. (with E. Savelev), Control of homogeneous shear flow of multimode Maxwell fluids, J. Non-Newtonian Fluid Mech.
2. The high Weissenberg number limit of the upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech.

F. Conference Papers
1. Bifurcation of singular and transient solutions: spatially non-periodic patterns for chemical reaction models in infinitely extended domains, in: H. Berestycki and H. Brézis (eds.), Recent Contributions to Nonlinear Partial Differential Equations, Pitman Research Notes in Mathematics 50, 1981, pp. 172-216
2. Theory and numerics of a quasilinear parabolic equation in rheology, in: K.B. Hannsgen et al. (eds.), Volterra and Functional Differential Equations, Marcel Dekker, 1982, pp. 287-310
3. Initial value problems for viscoelastic liquids, in: P.G. Ciarlet and M. Roseau (eds.): Trends and Applications of Pure Mathematics to Mechanics, Springer Lecture Notes in Physics 195, 1984, pp. 333-345
4.(with P. Markowich), The stretching and break-up of filaments of polymer solutions in a pendent drop experiment, in: B. Mena, A. Garcia-Rejon and C. Rangel-Nafaile (eds.), Advances in Rheology, Vol. 1: Theory, Universidad Nacional Autonoma de Mexico 1984 (Elsevier 1985), pp. 677-682
5. Slow steady flows of viscoelastic liquids with constitutive equations of Maxwell or Jeffreys type, in: N.S. Trudinger and G. Williams (eds.), Miniconference on Nonlinear Analysis, Proc. of the Centre for Mathematical Analysis, Vol. 8, Australian National University 1984, pp. 191-194
6. Recent developments and open problems in the mathematical theory of viscoelasticity, in: A.S. Lodge, M. Renardy and J.A. Nohel (eds.), Viscoelasticity and Rheology, Academic Press 1985, pp. 345-360
7. (with W.J. Hrusa ), On a nonlinear hyperbolic integrodifferential equation with a singular kernel, in: V. Lakshmikantham (ed.), Trends in the Theory and Practice of Non-linear Analysis, North Holland 1985, pp. 193-200
8. (with W.J. Hrusa ), Propagation of singularities in linear viscoelasticity, in: C. Dafermos, J.L. Ericksen and D. Kinderlehrer (eds.), Amorphous Polymers and Non-Newtonian Fluids, IMA Vol. in Math. and its Appl., Vol. 6, Springer 1987, pp. 161-167
9. (with J.A. Nohel), Development of singularities in nonlinear viscoelasticity, in: C. Dafermos, J.L. Ericksen and D. Kinderlehrer (eds.), Amorphous Polymers and Non-Newtonian Fluids, IMA Vol. in Math. and its Appl., Vol. 6, Springer 1987, pp. 139-152
10. Existence of steady flows of viscoelastic fluids and the question of inflow boundary conditions, in: J. Chandra and R. Srivastav (eds.), Constitutive Models of Deformation, SIAM 1987, pp. 150-155
11.Boundary conditions for steady flows of non-Newtonian fluids, in: P.H.T. Uhlherr (ed.), Xth Int. Congr. Rheol., Sydney 1988, Vol. 2, pp. 202-204
12. (with W.J. Hrusa ), A model problem in one-dimensional viscoelasticity with a singular kernel, in: G. da Prato and M. Iannelli (eds.), Volterra Integrodifferential Equations in Banach Spaces and Applications, Pitman Research Notes in Mathematics 190, 1989, pp. 221-230
13.An initial-value problem in viscoelasticity with a non-integrable memory function, in: A.R. Aftabizadeh (ed.), Differential Equations and Applications, Ohio University Press 1989, Vol. 2, pp. 333-336
14. A well-posed boundary value problem for supercritical flow of viscoelastic fluids of Maxwell type, in: B. Keyfitz and M. Shearer (eds.), Nonlinear Evolution Equations that Change Type, IMA Vol. in Math. and its Appl., Vol. 27, Springer 1990, pp. 181-191
15. Boundary conditions for steady flows of viscoelastic fluids, in: K. Kirchgässner (ed.), Problems Involving Change of Type, Springer Lecture Notes in Physics 359, 1990, pp. 133-138
16. Integration of the constitutive law of the Maxwell fluid near a corner, in: D.A. Siginer et al. (eds.), Developments in Non-Newtonian Flows, AMD-Vol. 175, ASME 1993, pp. 37-38
17. Linear stability of hyperbolic PDEs and viscoelastic flows, Proc. 14th IMACS World Congress on Computational and Applied Mathematics, Vol. 2, Georgia Tech 1994, pp. 894-897
18. (with Y. Renardy), Sideband instabilities in two-fluid flows, in: A. Narain, D. Siginer and K.M. Kelkar (eds.), Two-Fluid Flows with or without Phase Change, AMD-Vol 184, ASME 1994, pp. 55-60
19. (with Y. Renardy), Instabilities in two-layer channel flows, in: A. Doelman and A. van Harten (eds.), Nonlinear Dynamics and Pattern Formation in the Natural Environment, Pitman Research Notes in Mathematics 335, 1995, pp. 238-256
20. Asymptotic evolution and breakup of Newtonian and viscoelastic jets, in: Y. Renardy, A.V. Coward, D.T. Papageorgiou and S.M. Sun (eds.), Advances in Multi-Fluid Flows, SIAM 1996, pp. 310-315
21. High Weissenberg number boundary layers and corner singularities in viscoelastic flows, in: M.J. Adams, R.A. Mashelkar, J.R.A. Pearson and A.R. Rennie (eds.), Dynamics of Complex Fluids, Imperial College Press - The Royal Society 1998, pp. 37-45
22. Corner singularities and high Weissenberg number asymptotics for viscoelastic fluids, in: D. Siginer and S.G. Advani (eds.), Rheology and Fluid Mechanics of Nonlinear Materials, AMD-Vol 217, ASME 1996, pp. 71-73
23. High Weissenberg number asymptotics and corner signularities in viscoelastic flows, in: D. Durban and J.R.A. Pearson (eds.), Non-Linear Singularities in Deformation and Flow, Kluwer 1999, pp. 13-20
24. (with T. Hagen), On the equations of fiber spinning in nonisothermal viscous flow, in: J. Escher and G. Simonett (eds.), Topics in Nonlinear Analysis. The Herbert Amann Anniversary Volume, Birkhäuser 1999, pp. 321-348
25. (with T. Hagen), Stability issues in nonisothermal elongational flow, in: J. Bona, K. Saxton and R. Saxton (eds.), Nonlinear PDEs, Dynamics and Continuum Physics, Contemporary Mathematics 255, Amer. Math. Soc. 2000, pp. 97-108
26. (with T. Hagen), On the equations of melt-spinning in viscous flow, in: J. Nečas, W. Jäger and J. Stara (eds.), Partial differential equations (Praha, 1998), Chapman & Hall/CRC 2000, pp. 147-157
27. (with T. Hagen), Eigenvalue asymptotics in fiber spinning, in: D.M. Binding et al. (eds.), Proc. XIIIth Int. Congr. Rheol, British Society of Rheology 2000, Vol. 2. pp. 330-332
28. Breakup and non-breakup of jets, in: D.M. Binding et al. (eds.), Proc. XIIIth Int. Congr. Rheol, British Society of Rheology 2000, Vol. 2. pp. 337-338
29. (with T. Hagen), On the non-isothermal formation of polymeric fibers, in: B. Fiedler et. al. (eds.), EQUADIFF 99, Proc. Int. Conf. Diff. Eqs. (Berlin, 1999), Vol. 2, World Scientific, Singapore 2000, pp. 1126-1128
30. Surface tension driven breakup of viscoelastic jets, in: W.Z. Chien, C.J. Cheng, S.Q. Dai, X.M. Guo and L.Y. Dong (eds.), Proc. 4th Internat. Conf. Nonlinear Mech., Shanghai University Press 2002, pp. 129-131
31. Breakup asymptotics of viscoelastic jets, in: H. Münstedt, J. Kaschta and A. Merten (eds.), Proc. 6th Eur. Conf. Rheol., Erlangen 2002, pp. 43-44
32. (with Y. Renardy, T. Chinyoka, D.B. Khismatullin and J. Li), A viscoelastic VOF-PROST code for the study of drop deformation, Proc. 2004 ASME Heat Transfer/Fluids Engineering Summer Conf., Charlotte, NC, July 2004, Paper HT-FED2004-56114
33. Breakup of non-Newtonian liquid jets with inertia, Proc. XIVth Int. Congr. Rheol., Paper NF04, Korean Society of Rheology 2004
34. Nonlinear perturbations of partially controllable systems, in: O. Emanouvilov, G. Leugering, R. Triggiani and B. Zhang, Control Theory of Partial Differential Equations, Lecture Notes in Pure and Applied Mathematics, CRC Press 2005, pp. 157-167
35. Global existence and stability results for viscoelastic shear flows, in: W.Z. Chien, S.Q. Dai, Z.W. Zhou and C.J. Cheng (eds.), Proc. 5th Internat. Conf. Nonlinear Mech., Shanghai University Press 2007, pp. 99-101
36. Draw resonance revisited, Second International Symposium on Instability and Bifurcations in Fluid Dynamics, J. Phys. Conf. Ser. 64
37. Are viscoelastic flows under control or out of control?, in: D. Konate (ed.), Mathematical Modeling, Simulation, Visualization and e-Learning, Springer 2008, pp. 201-208
38. (with J.R. Waldmeyer, M.R. Mackley and Y. Renardy), Numerical simulation of the deformation and break-up of droplets subjected to complex, time dependent strain rates, in: A. Co, L.G. Leal, R.H. Colby and A.J. Giacomin (eds.), The XVth International Congress on Rheology, AIP Conference Proceedings 1027, American Institute of Physics 2008, pp. 875-877
39. (with S. Afkhami, Y. Renardy, J.S. Riffle and T. St. Pierre), Numerical modeling of ferrofluid droplets in magnetic fields, in: A. Co, L.G. Leal, R.H. Colby and A.J. Giacomin (eds.), The XVth International Congress on Rheology, AIP Conference Proceedings 1027, American Institute of Physics 2008, pp. 884-886
40. On the use of Laplace transform inversion for reconstruction of relaxation spectra, in: A. Co, L.G. Leal, R.H. Colby and A.J. Giacomin (eds.), The XVth International Congress on Rheology, AIP Conference Proceedings 1027, American Institute of Physics 2008, pp. 1367-1368

G. Published contributions to problem columns
1. Limit of a power of a matrix, SIAM Review 26 (1984), p. 121
2. Conjectured trigonometrical identities, SIAM Review 29 (1987), pp. 132-135
3. Zero of least modulus, SIAM Review 31 (1989), pp. 126-127
4. Problem of the Nile, SIAM Review 32 (1990), p. 303
5. Two determinant inequalities, SIAM Review 32 (1990), pp. 681-682
6. On the number of roots of a transcendental equation, SIAM Review 32 (1990), pp. 682-683
7. Linear system with positive solutions, SIAM Review 34 (1992), pp. 500-502
8. On winning in the game of lotto, SIAM Review 35 (1993), pp. 137-139
9. Asymptotic solution of the telegraph equation, SIAM Review 35 (1993), pp. 306-307
10. A convex set, SIAM Review 36 (1994), p. 111
11. An integral relation for successive eigenvalues, SIAM Review 36 (1994), p. 497
12. An operator limit, SIAM Review 36 (1994), p. 659
13. A unique real root, SIAM Review 36 (1994), pp. 661-662
14. A characterization of uniformly accelerated motion, SIAM Review 38 (1996), pp. 525-526
15. Existence and uniqueness for a boundary value problem, SIAM Review 39 (1997), pp. 136-138
16. An inequality, SIAM Review 40 (1998), p. 729
17. (with T. Hagen), A calculus exam misprint, SIAM Electronic Problems and Solutions
18. An elementary version of the Landesman-Lazer theorem (solution), SIAM Electronic Problems and Solutions
19. Rolewicz's problem (solution), SIAM Electronic Problems and Solutions
20. A problem from Blacksburg Middle School, SIAM Electronic Problems and Solutions
21. A characterization of groups (solution), SIAM Electronic Problems and Solutions
22. An integral involving the product of five Bessel functions (solution), SIAM Electronic Problems and Solutions
23. A simple proof of an asymptotic formula for a sum of cosecants (solution), SIAM Electronic Problems and Solutions
24. Harmonic functions with Cauchy-Riemann boundary data (solution), SIAM Electronic Problems and Solutions

H. Book reviews
1. H. Brézis and J.L. Lions (eds.), Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. IX, Pitman Research Notes in Mathematics 181, 1988, in: Z. angew. Math. Phys. 40 (1989), p. 790
2. V. Boffi and H. Neunzert (eds.), Application of Mathematics in Industry and Technology, Teubner 1989, in: Z. angew. Math. Phys. 41 (1990), p. 155
3. W. Chien and Z. Fu (eds.), The Advances of Applied Mathematics and Mechanics in China, Vol. 1, China Academic Publ. 1987, in: Z. angew. Math. Phys. 41 (1990), p. 606
4. J. Dunwoody, Elements of Stability of Viscoelastic Fluids, Pitman Research Notes in Mathematics 213, 1989, in: Z. angew. Math. Phys. 41 (1990), p. 930
5. E. Zeidler, Nonlinear Functional Analysis and its Applications; Vol. II/A: Linear Monotone Operators and II/B: Nonlinear Monotone Operators, Springer 1990, in: Z. angew. Math. Phys. 42 (1991), p. 157
6. D.D. Joseph, Fluid Dynamics of Viscoelastic Fluids, Springer 1989, in: Z. angew. Math. Phys. 42 (1991), p. 157
7. A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer, 2nd ed. 1990, in: Z. angew. Math. Phys. 42 (1991), p. 630
8. B.L. Keyfitz and M. Shearer (eds.), Nonlinear Evolution Equations that Change Type, IMA Vols. in Math. and its Appl., Vol. 27, Springer 1990, in: Z. angew. Math. Phys. 42 (1991), p. 808
9. V.G. Mazya and S.M. Nikolskii (eds.), Analysis IV, Springer 1991, in: Z. angew. Math. Phys. 43 (1992), p. 589
10. B. Straughan, The Energy Method, Stability and Nonlinear Convection, Springer 1992, in: Z. angew. Math. Phys. 44 (1993), p. 187
11. J.F. Rodrigues and A. Sequeira (eds.), Mathematical Topics in Fluid Mechanics, Pitman Research Notes in Mathematics 274, 1992, in: SIAM Review 36 (1994), pp. 139-140
12. J.M. Chadam and H. Rasmussen (eds.), Free Boundary Problems in Fluid Flow with Applications, Pitman Research Notes in Mathematics 282, 1993, in: Z. angew. Math. Phys. 45 (1994), p. 345
13. G.P. Galdi and J. Nečas (eds.), Recent Developments in Theoretical Fluid Mechanics, Pitman Research Notes in Mathematics 291, 1993, in: Z. angew. Math. Phys. 45 (1994), p. 502
14. A.L. Yarin, Free Liquid Jets and Films: Hydrodynamics and Rheology, Longman 1993, in: Z. angew. Math. Phys. 45 (1994), p. 503
15. L.M. Brekhovskikh and V. Goncharov, Mechanics of Continua and Wave Dynamics, Springer, 2nd ed. 1994, in: Z. angew. Math. Phys. 45 (1994), p. 992
16. S. Antman, Nonlinear Problems of Elasticity, Springer 1995, in: SIAM Review 37 (1995), p. 637
17. A. Kulikovskii and E. Sveshnikova, Nonlinear Waves in Elastic Media, CRC Press 1995, in: SIAM Review 39 (1997), p. 358
18. G.P. Galdi, J. Màlek and J. Nečas (eds.), Mathematical Theory in Fluid Mechanics, Pitman Research Notes in Mathematics, Longman 1996, in: Z. angew. Math. Phys. 48 (1997), p. 699
19. A.Ya. Shklyar, Complete Second Order Linear Differential Equations in Hilbert Spaces, Birkhäuser 1997, in: SIAM Review 40 (1998), p. 175
20. G.L. Lamb, Introductory Applications of Partial Differential Equations, Wiley 1995, in: Z. angew. Math. Phys. 49 (1998), pp. 339-340
21. F. Scheck, Mechanik, Springer 1996, in: Z. angew. Math. Phys. 49 (1998), p. 681
22. J.L. McCauley, Classical Mechanics, Cambridge University Press 1997, in: Z. angew. Math. Phys. 49 (1998), p. 1005
23. B. Straughan, Explosive Instabilities in Mechanics, Springer 1998, in: J. Fluid Mech. 377 (1998), pp. 380-381
24. S.N. Antontsev, J.I. Diaz and S.I. Shmarev, Energy Methods in Continuum Mechanics, Kluwer 1996, in: Z. angew. Math. Phys. 50 (1999), p. 339
25. H.K. Kuiken (ed.), The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz, Kluwer 1996, in: Z. angew. Math. Phys. 50 (1999), p. 675
26. V.I. Arnold and B.A. Khesin, Topological Methods in Hydrodynamics, Springer 1998, in: Z. angew. Math. Phys. 50 (1999), p. 675
27. L.N. Hand and J.D. Finch, Analytical Mechanics, Cambridge University Press 1998, in: Z. angew. Math. Phys. 51 (2000), p.505
28. R. Meyer-Spasche, Pattern Formation in Viscous Flows, Birkhäuser 1999, in: Z. angew. Math. Phys. 52 (2001), p. 897
29. S. Friedlander and D. Serre (eds.), Handbook of Mathematical Fluid Dynamics, Vol. 1, North Holland 2002, in: J. Fluid Mech. 480 (2003), pp. 335-336
30. J. Jost, Partial Differential Equations, Springer 2002, in: SIAM Review 45 (2003), pp. 376-377
31. J.R. Ockendon et al., Applied Partial Differential Equations, Oxford University Press, Revised Edition 2003, in: Z. angew. Math. Mech. 84 (2004), p. 216
32. D.M. Klimov and V.Ph. Zhuravlev, Group-Theoretic Methods in Mechanics and Applied Mathematics, Taylor and Francis 2002, in: Z. angew. Math. Phys. 55 (2004), p. 363
33. A.A. Samarskii and A.P. Mikhailov, Principles of Mathematical Modeling, Taylor and Francis 2002, in: Z. angew. Math. Phys. 55 (2004), p. 364
34. S. Friedlander and D. Serre (eds.), Handbook of Mathematical Fluid Dynamics, Vol. 3, North Holland 2004, in: J. Fluid Mech. 527 (2005), pp. 378-379
35. R.M. Temam and A.M. Miranville, Mathematical Modeling in Continuum Mechanics, 2nd ed., Cambridge University Press 2005, in: SIAM Review 48 (2006), p. 429
36. J. Jost, Partial Differential Equations, 2nd ed., Springer 2007, in: SIAM Review 49 (2007), p. 539
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Curriculum Vitae of MICHAEL RENARDY

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I am an editor of the following journals and book series:

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Publications

A. Books

B. Books Edited

C. Invited Reviews

D. Papers in Scientific Journals

E. Submitted for Publication

F. Conference Papers

G. Published contributions to problem columns

H. Book reviews