Location
Online (message amgrad@uwaterloo.ca for link)
Candidate
Shri Lal Raghudev Ram Singh | Applied Mathematics, University of Waterloo
Title
Stabilization of Linear and Nonlinear Partial Differential Equations (PDEs)
Abstract
Stabilization results for abstract linear and nonlinear evolution equations have significant applications in the analysis and control of various mathematical models described by partial differential equations. The purpose of this seminar is threefold. First, I will introduce the notion of stability for semigroups and their characterizations, along with associated functional analytic tools such as unique continuation, La Salle’s invariance principle, the Gearhart-Huang-Prüss theorem, and the Arendt-Batty stability criterion. Second, I will discuss methods for PDE stabilization, review relevant background literature, and briefly outline potential research directions for future work. Lastly, I will present our preliminary work on the linear stabilization problem in abstract spaces, demonstrating the robustness of exponential stability under perturbations, followed by an application to a singular/degenerate parabolic problem. This result further extends Gibson’s stability theorem (1980) and its extension by Alabau-Cannarsa (2013) by relaxing the compactness and boundedness conditions on perturbations.