Global existence for the wave equation with nonlinear boundary damping and source terms

The paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms. The typical problem studied is [GRAPHICS] where Omega subset of R-n (n greater than or equal to 1) is a regular and bounded domain, alphaOmega = Gamma(0) boolean OR Gamma(1), m > 1, 2 less than or equal to p < r, where r = 2(n - 1)/(n - 2) when n greater than or equal to 3, r = infinity when n = 1, 2, and the initial data are in the energy space. We prove local existence of the solutions in the energy space when m > r/(r + 1 - p) or n = 1, 2, and global existence when p less than or equal to m or the initial data are inside the potential well associated to the stationary problem. (C) 2002 Elsevier Science (USA). All rights reserved.