Blow up in a nonlinear viscoelastic wave equation with strong damping and variable sources

Tóm tắt

This paper is devoted to studying the finite-time blow-up in high initial energy for the solution of the nonlinear viscoelastic wave equation

 u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds-\Delta u_{t}=|u|^{p(x)-2}u,

in a bounded domain $\Omega\subset\R^n$.  Our result improves the blow-up result in the previous work that was obtained by Nhan-Truong-Y [Appl. Anal., 102 (3) (2023), 782-799].

Keywords: Nonlinear wave equation; Viscoelasticity; Blow-up; Strong damping; Variable exponent sources.