Polynomial stabilizations for wave equations with positive definite kernels and boundary frictional damping

Abstract

This paper is concerned with stabilizations of wave equations with variable coefficients, subject to positive definite kernels and boundary frictional damping. Here, the memory kernel can be sign‐varying and the boundary of the domain does not need to satisfies the “geometric control condition.” Under some appropriate assumptions on memory kernel, we establish the polynomial stabilizations. Meanwhile, the decay result shows that the memory damping plays the dominant role in the stabilizations of the system with both memory damping and boundary frictional damping.