Visco‐elastic damped wave models with time‐dependent coefficient

Abstract

In this paper, we study the following Cauchy problem for linear visco‐elastic damped wave models with a general time‐dependent coefficient : We are interested to study the influence of the damping term on qualitative properties of solutions to () as decay estimates for energies of higher order and the parabolic effect. The main tools are related to WKB‐analysis. We apply elliptic as well as hyperbolic WKB‐analysis in different parts of the extended phase space.