首页|Life-Spans and Blow-Up Rates for a p-Laplacian Parabolic Equation with General Source
Life-Spans and Blow-Up Rates for a p-Laplacian Parabolic Equation with General Source
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This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian ut-▽·(|▽u|p-2▽u)=f(u),where p ≥ 2 and the function f(u)satisfiesα∫u0f(s)ds≤uf(u)+βup+γ,u＞0 for some positive constants α,β,γ with 0＜β ≤(α-p)λ1,p/p,which has been studied under the initial condition Jp(uo)＜0.This paper generalizes the above results on the follow-ing 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.
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