Life-Spans and Blow-Up Rates for aρ-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 p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β,γwith 0<■,which has been studied under the initial condition Jp(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 for p=2;some new lifespans and upper blow-up rates are given under certain conditions.