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.
"Energy decay for solutions of the wave equation with general memory boundary conditions." Differential Integral Equations 22 (11/12) 1173 - 1192, November/December 2009. https://doi.org/10.57262/die/1356019411