Dynamics of a coupled system for nonlinear damped wave equations with variable exponents

Abstract

AbstractWe consider a coupled system of viscoelastic wave equation with weak, strong damping and power nonlinearity. For a single viscoelastic wave equation, we have already obtained a global solution, its decay rate and finite‐time blow‐up [1]. In this paper, we extend these results to a coupled system. First, we obtain a global solution and derive its decay rate by a decreasing energy. Finally, we apply the concavity method in order to show that the solution blows up in finite time under nonclassic constraint on kernel functions.