WEAK INPUT TO STATE ESTIMATES FOR 2D DAMPED WAVE EQUATIONS WITH LOCALIZED AND NONLINEAR DAMPING

摘要

In this paper, we study input-to-state stability (ISS) issues for damped wave equations with Dirichlet boundary conditions on a bounded domain of dimension two. The damping term is assumed to be nonlinear and localized to an open subset of the domain. We handle the disturbed case as an extension of [Martinez and Vancostenoble, Port. Math., 57 (2000), pp. 285{310], where stability results are given with a damping term active on the full domain with no disturbances considered. We provide ISS types of results.