Global solutions and blow-up for a coupled system of nonlinear hyperbolic equations with weak damping

This paper investigates a coupled system of nonlinear hyperbolic equations with weak damping. It is shown that the global solution and finite time blow-up solution exist at subcritical or critical initial energy. Moreover, the finite time blow-up result at arbitrarily high initial energy is obtained. Also, we derive the exponential energy decay estimation of the global solution and estimate the upper and lower bounds of the blow-up time.