Existence of global-solutions to some nonlinear dissipative wave-equations

Abstract

Let Omega be a smooth bounded domain. We prove existence of global solutions, i.e., solutions defined for all t epsilon R, for dissipative wave equations of the form: u'' - Delta u + \u'\(p-1) u' = 0 in Omega x (-infinity, infinity), p > 1, with Dirichlet boundary conditions. When Omega is unbounded the same existence result holds for p greater than or equal to 2.