Location
DC 1304
Candidate
Shri Lal Raghudev Ram Singh | Applied Mathematics, University of Waterloo
Title
Stabilization of Linear and Nonlinear Partial Differential Equations
Abstract
Many physical, engineering, and industrial phenomena such as elastic structures including plates, beams, and membranes, wave propagation models, diffusion processes, and climate dynamics are governed by partial differential equations.These systems naturally give rise to linear and nonlinear infinite dimensional evolution equations and often exhibit unstable behavior due to their distributed structure and complex dynamics. Understanding their stability and robustness under perturbations is therefore a central problem in the analysis and control of such systems. In this presentation, the discussion will be fourfold. First, I will briefly introduce the research methodology together with the main mathematical tools that will be used throughout the talk. Second, I will review the background literature concerning the lack of uniform stabilization for linear infinite dimensional systems. Third, I will present our abstract results and illustrate their applicability through an example involving coupled plate dynamics. Finally, I will outline the proposed research directions, focusing on the robustness of polynomial stability in Hilbert and Banach spaces and on the stabilization of nonlinear infinite dimensional systems.