Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations

Abstract

In this work, we consider an initial-boundary value problem related to the nonlinear coupled viscoelastic equations        |u t | j u tt − ∆u tt − div |∇u| α−2 ∇u − ∆u + t 0 g (t − s) ∆uds + |u t | m−1 u t = f 1 (u, v) , |v t | j v tt − ∆v tt − div |∇v| β −2 ∇v − ∆v + t 0