Systems of nonlinear wave equations with damping and source terms

Abstract

In this article we focus on the global well posedness of the system of nonlinear wave equations \begin{align*} u_{tt}- \Delta u + |u_{t}|^{m-1} u_{t}= f_{1}(u,v)\\ v_{tt}- \Delta v + |v_{t}|^{r-1} v_{t}= f_{2}(u,v) \end{align*} in a bounded domain $\Omega\subset\mathbb{R}^{n}$, $n = 1,2,3,$ with Dirichlét boundary conditions. Under some restriction on the parameters in the system we obtain several results on the existence of local and global solutions, uniqueness, and the blow up of solutions in finite time.