Blow up of positive initial-energy solutions to systems of nonlinear wave equations with degenerate damping and source terms

Abstract

Blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms supplemented with the initial and Dirichlet boundary conditions is shown in [13], in a bounded domain \Omega \subset R^n, where n = 1; 2; 3 and the initial energy is negative. Our result extends this previous recent resul where we will prove that the solution blows up for all time provided that the initial data are large enough in bounded domain of R^n; where (n \geq 1) ; with positive initial energy and the strong nonlinear functions f_1 and f_2 satisfying appropriate conditions. The main tool of the proof is based on a methods used in [19] developed in [9], [14].