A sharper decay rate for a viscoelastic wave equation with power nonlinearity

Abstract

We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo‐Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex.