Professor Burns' current research is focused on computational methods for modeling, control, estimation and optimization of complex systems where spatially distributed information is essential. This includes systems modeled by partial and delay differential equations. Recent applications include modeling and control of thermal fluids, design and thermal management systems and optimization of mobile sensor networks.
Professor Liu's research focuses on the design of effective low-dimensional reduced models for nonlinear deterministic and stochastic PDEs as well as DDEs. Applications to classical and geophysical fluid dynamics are actively pursued. Particular problems that are addressed include bifurcation analysis, phase transition, surrogate systems for optimal control, and stochastic closures for turbulence.
Dr. Malik's interests lie in nonlinear partial differential equations; specifically the asymptotic behavior, orbital stability, and effective dynamics, of dark solitons that arise from defocusing nonlinear Schrodinger equations.
Dr. Teffera Asfaw conducts research in nonlinear analysis. The main research areas are degree and variational inequality theories and applications. The goal of the research is to derive existence theorems for inclusion and inequality problems and their applications to operator equations and inequalities in appropriate function spaces.