Growth of Solutions to System of Nonlinear Wave Equations with Degenerate Damping and Strong Sources

Abstract

M. A. Rammaha and Sawanya Sakuntasathien, [{\it Global existence and blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms}, Nonlinear Analysis 72(2010)2658-2683], introduced and studied the concept of existence and nonexistence of solutions in a bounded domain $\Omega \subset R^{n}$, $n=1,2,3$. In the present work we will prove that the solutions of system of nonlinear wave equations with degenerate damping and source terms supplemented with the initial and Dirichlet boundary conditions grows exponentially in a bounded domain $\Omega \subset R^{n},n>0$, provided that the initial data are large enough, with positive initial energy and the strong nonlinear functions $f_{1}$ and $f_{2}$ satisfying appropriate conditions.