Observability and Stabilization of 1-D Wave Equations with Moving Boundary Feedback

摘要

In this paper, we are concerned with a wave equation on a time-dependent domain with a Dirichlet boundary condition at the endpoint x = 0 and a boundary feedback at the moving endpoint x = kt. We discuss the stabilization and exact boundary observability of the 1-dimensional wave equation with moving boundary feedback. By using generalized Fourier series and Parseval's equality in weighted L-2-spaces, we derive a precise polynomial asymptotic stability for the energy function of the solution. Moreover, the exact boundary observabilities of the solution are established in minimal time. The observability constants are explicitly given at each endpoint.