Energy decay for solutions of the wave equation with general memory boundary conditions

Abstract

We consider the wave equation in a smooth domain subject to Dirichlet boundary conditions on one part of the boundary and dissipative boundary conditions of memory-delay type on the remainder of the boundary, where a general Borel measure is involved. Under quite weak assumptions on this measure, using the multiplier method and a standard integral inequality, we show the exponential stability of the system. Some examples of measures satisfying our hypotheses are given, recovering and extending some of the results from the literature.