Intrinsic decay rate estimates for abstract wave equation with memory

摘要

In this paper, we consider an abstract wave equation in the presence ofmemory. The viscoelastic kernel g(t) is subject to a general assumption g;(t) <=-H(g(t)),where the function H(.) is an element of C-1(R+) is positive, increasing and convex with H(0)=0. We give the decay result as a solution to a given nonlinear dissipative ODE governed by the function H(s). Copyright (C) 2017 JohnWiley & Sons, Ltd.