Estimates for the life-span of the solutions for some semilinear wave equations

In this paper we prove main result on blow-up rates, blow-up constants and some estimates for life-spans of the solutions for some initial-boundary value problems for semi-linear wave equations. Under some conditions the life-span T* can be estimated by beta (k, alpha) := min {2(3/2+1/2 alpha) center dot delta (k,alpha) a (0) a' (0)(-1) : k is an element of (0, 1) }, where a(0) = integral(Omega) u(0) (x)(2) dx, a' (0) = 2 integral(Omega) u(0) (x) u(1) (x) dx and delta (k, alpha) is given by delta (k, alpha) := 1/k (k(2)/1-k(2)) (alpha/1+2 alpha) ( 1- ( 1+ (1/k(2) - 1) (alpha/1+2 alpha)) (-1/2 alpha) ).