Stabilization of the wave equation with moving boundary

摘要

AbstractWe deal with the wave equation with assigned moving boundary (0 ce:italic>xce:italic>a(t)) upon which Dirichlet–Neuman boundary conditions are satisfied, herea(t) is assumed to move slower than light and periodically. We give a feedback which guarantees the exponential decay of the energy. The proof relies on a reduction theorem by Ammari et al. (2017) and Yoccoz (1984) . At the end we give a remark on the moving-pointwise stabilization problem.