In this article we focus on the global well posedness of the system of nonlinear wave equations u_(tt)-Δu+|u_t|~(m-1)ut=f_1(u,v) u_(tt)-Δu+|u_t|~(r-1)ut=f_2(u,v) in a bounded domain Ω C R~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.
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