Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms

Abstract

We study the Cauchy problem tor the nonlinear wave equation with nonlinear damping au t | u t | m−1 and a nonlinear source term of type ba| a| p−1 . When existence result is established for any initial data. When 1 < m < p. a finite time blow-up result is proved for compactly supported data with negative initial energy.