Systems of nonlinear wave equations with damping and source terms. (English) Zbl 1212.35268

Summary: In this article we focus on the global well posedness of the system of nonlinear wave equations \(u_{tt}-\Delta u+| u_t| ^{m-1}u_t=f_1(u,v)\), \(v_{tt}-\Delta v+| v_t| ^{r-1}v_t=f_2(u,v)\) in a bounded domain \(\Omega \subset \mathbb R^n\), \(n=1,2,3\), with Dirichlet 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.


35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations