Global non-existence of solutions of a class of wave equations with non-linear damping and source terms

In this paper we consider the non-linear wave equation u(n) - Deltau(t) - div(\delu\(alpha-2)deluU) - div(\delu(t)\(beta-2)delu(t)) + a\u(t)\(m-2)u(t)=b\u\(p-2)u a, b > 0. associated with initial and Dirichlet boundary conditions. We prove, under suitable conditions on alpha, beta, m, p and for negative initial energy, a global non-existence theorem. This improves a result by Yang (Math. Meth. Appl. Sci. 2002; 25:825-833), who requires that the initial energy be sufficiently negative and relates the global non-existence of solutions to the size of Omega. Copyright (C) 2004 John Wiley Sons, Ltd.