A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions

Abstract

Abstract In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g, the function Φ, p>max{ρ+2,m,q,2} $p > \max \{ \rho +2, m, q,2\}$, and the initial data, we prove a global nonexistence of solutions for a quasilinear viscoelastic wave equation with positive initial energy.

Keywords

• Global nonexistence of solution
• Blow-up of solution
• Quasilinear viscoelastic wave equation
• Acoustic boundary conditions