Global nonexistence of positive initial energy solutions for a viscoelastic wave equation

摘要

In this paper, we consider the nonlinear viscoelastic equation: vertical bar u(t)vertical bar(rho)u(tt) - Delta u +integral(t)(0) g(t - tau) Delta u(tau)d tau + vertical bar u(t)vertical bar(m) (2)u(t) = vertical bar u vertical bar(P) (2)u , in Omega x [0,T], with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g, we prove the nonexistence of global solutions with positive initial energy. (C) 2015 Elsevier Ltd. All rights reserved.