EXISTENCE OF GLOBAL-SOLUTIONS TO SOME NONLINEAR DISSIPATIVE WAVE-EQUATIONS

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