New decay result for the viscoelastic wave equation with a nonlinear source and new conditions on the relaxation function

Abstract

This In this work, we consider a viscoelastic wave equation with a nonlinear source. Under a new condition on the relaxation function which is g ' (t) ≤ −H(g(t)) where H is a positive increasing and not necessarily convex function, we establish a new stability result which rely on the multiplier method. We arrive at more general result than ones in the previous published studies.