Gazi Mahmud Alam

My interest in research is focused on control problems for partial differential equations on quantum graphs. Under quantum graphs, we understand differential operators on geometric graphs, coupled by certain vertex matching conditions. Network-like structures play a fundamental role in many problems of science and engineering. The classical problem here that comes from applications is the problem of oscillations of flexible structures made of strings, beams, cables, and struts. These models describe bridges, space-structures, antennas, transmission-line posts, steel-grid reinforcements, and other typical objects of civil engineering. Control and inverse theories constitute an important part of this rapidly developing area of applied mathematics — analysis on graphs. They are tremendously important for all applications, as mentioned above. Networks of the telegrapher equations have been recently used for modeling electrical circuits and arterial blood flows. Very little is known about the controllability of such networks. Currently, I am working on the forward, control, and inverse problem for the power grid networks.