Blow-up Rate For A Semi-linear Wave Equation In Bounded Domain

In this paper,the blow-up rate for the semi-linear wave equation utt一△u=|u|p-1u is obtained in the bounded domain.Using the transformation ω(s,y)=(T-t)2/(p-1)u(t,x),s= 1/(T-t),山e system is translated into another wave equation. Via the blow-up analysis and energy estimate,we have obtained the bound of ω,and the inverse of transformation gives the bound of u provided the exponent p>1.Moreover we can get the blow-up rate of ▽u and ut provided 1<p<1+4/(N-1) for N≥3 or 1<p<5 for 1≤N≤2 with the same method.