Observability for the Wave Equation with Variable Support in the Dirichlet and Neumann Cases

摘要

We study the observability of the wave equation when the observation set changes over time. For the one dimensional Neumann problem, using Fourier series, we are able to prove for the exact observability an equivalent condition already known for the Dirichlet problem; see [1]. For the observability problem with Dirichlet boundary conditions, we focus on multidimensional problems and the observability inequality is proven through a multiplier approach. Besides this, we present some applications and a numerical simulation.