Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms

Abstract 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 ≤ 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.