EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

We study the nonlinear wave equation involving the nonlinear damping term u(t)\u(t)\m-1 and a source term of type u\u\p-1. For 1 < p less-than-or-equal-to m we prove a global existence theorem with large initial data. For 1 < m < p a blow-up result is established for sufficiently large initial data. (C) 1994 Academic Press, Inc.