Asymptotic behavior of one-dimensional wave equations with set-valued boundary damping

Speaker: Prof. Dr. Yacine Chitour
Affiliation: Université Paris-Saclay, France
Organized by: FAU CAA-AvH, Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)

Zoom meeting link
Meeting ID: 681 0483 1646 | PIN code: 018906

Abstract. This talk concerns one dimensional wave equations with nonlinear boundary damping . After providing a brief summary of some important previous works, we will present a new framework for addressing associated well-posedness and stability issues. We shall consider wave equations in Lp functional spaces and with set-valued boundary dampings, which are a natural generalization of nonlinear dampings allowing to fully exploit some symmetry properties previously observed and for which we can provide the most general well-posedness and existence results. We will show how our techniques allow us to retrieve known results on the asymptotic behavior and provide answers to previously open questions. In particular, we provide a complete characterization of the asymptotic behavior of systems in which the boundary condition is described by the sign function and we also address input-to-state stability with respect to boundary perturbations. This talk is based on joint works with Swann Marx and Guilherme Mazanti.