报告人：Guilherme Afonso MAZANTI，INRIA Saclay-île-de-France（法国国家信息与自动化研究所）

报告时间：3 月10日14：30-15：30

报告地点：管理楼1418教室

报告题目：Wave equations with nonsmooth boundary conditions

报告摘要： Wave equations with nonlinear boundary conditions have been the subject of several works in the past decades due to their importance from both theoretical and applied points of view. Nonlinear boundary conditions may arise in particular from nonlinear phenomena in the practical implementation of boundary control laws for linear wave equations, such as nonlinearities in the components used for the implementation or saturation phenomena, and they may have an important impact in the stability properties and the asymptotic behavior of the system.

In this talk, after providing a brief summary of some important previous works on wave equations with nonlinear boundary damping, we will present a new framework for addressing this problem in the case of equations in one space dimension. We shall consider wave equations in L^p functional spaces (including p = infinity) 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 some very general well-posedness results.

We will show how our techniques allow us to retrieve some known results on the asymptotic behavior of wave equations with nonlinear boundary damping and provide answers to previously open questions. In particular, we provide a description of the decay rate of solutions for several nonlinear boundary conditions and we completely characterize the asymptotic behavior in the case of a boundary condition described by the sign function. We will conclude with some open problems and perspectives.

This talk is based on a joint work with Yacine Chitour and Swann Marx.