Life-Spans and Blow-Up Rates for a p-Laplacian Parabolic Equation with General Source

This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with pp-Laplacian u(t)-del & sdot;(|del u|(p-2)del u)=f(u), where p >= 2and the function f(u) satisfies alpha integral u0f(s)ds <= uf(u)+beta u(p)+gamma,u>0 for some positive constants alpha,beta,gamma with 0<beta <=(alpha-p)lambda 1,pp, which has been studied under the initial conditionJp(u0)<0. This paper generalizes the above results on the following aspects: a new blow-up condition is given, which holds for all p>2; a new blow-up condition is given, which holds forp=2; some new lifespans and upper blow-up rates are given under certain conditions.