Anthony Hastir
project info:
Title : "Well-posedness of infinite-dimensional linear systems with nonlinear feedback"
Abstract : For a class of nonlinear partial differential equations (PDE's), we study the existence of solutions, and in particular, the well-posedness. The main idea is to use systems theory to write the nonlinear PDE as a well-posed infinite-dimensional linear system interconnected with a static nonlinearity. By a simple example, it is shown that well-posedness of the closed-loop system is not guaranteed. Well-posedness of the closed-loop system holds under some conditions on the nonlinearity and on the open-loop system. This result extends the works of Tucsnak and Weiss (2014) since it includes locally Lipschitz continuous nonlinearities. The result is applied to show well-posedness of a system consisting of a vibrating string with nonlinear damping at the boundary.
