In this paper, we consider the solution of a nonlinear hyperbolic equation with Dirichlet boundary condition in a bounded domain. Under some assumptions, we show that the solution of the above problem blows up in a finite time and its blow-up time goes to that of the solution of a certain differential equation when some parameters go to infinity. Finally, we give some numerical results to illustrate our analysis.

nonlinear hyperbolic equation, blow-up, convergence, numerical blow-up time.