Blow-up of Solutions of a Quasilinear Wave Equation with Nonlinear Dissipation

Abstract

In this paper we establish the blow up of solutions to the quasilinear wave equation with a nonlinear dissipative term u_{tt} - M(||A^{1/2}u||²_2)Au + |ut|^βu_t = |u|^pu x ∈ Ω, t > 0