Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms

In this paper, we study a nonlinear hyperbolic system with strong damping. Firstly, by use of the successive approximation method and a series of classical estimates, we prove the local existence and uniqueness of weak solution. Secondly, via some inequalities, applying the potential method and the concave method, we discuss the asymptotic and blow-up behavior of weak solution with different conditions.