On the Blowing-Up Of The Classical Solution For The Wave Equation With A Non Linear Source

In this paper we consider the following initial-boundary problem.where ? is a bounded domain in NR with smooth boundary ??, L is an elliptic operator where ??fs is a positive, increasing and convex function for the nonnegative values of sand ? is a positive parameter. 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 the one of the solution of the following differential equations:Finally, we give some numerical results to illustrate our analysis.