Systems of nonlinear wave equations with damping and source terms
Systems of nonlinear wave equations with damping and source terms
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 …