UNIVERSAL BOUNDS FOR POSITIVE SOLUTIONS OF DOUBLY DEGENERATE PARABOLIC EQUATIONS WITH A SOURCE

被引：0

作者：

Tedeev, A. F. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Appl Math & Mech, Str R Luksemburg 74, UA-340114 Donetsk, Ukraine

来源：

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE | 2011年 / 80卷 / 02期

关键词：

Degenerate parabolic equations; blow-up; universal bounds;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a doubly degenerate parabolic equation with a source term of the form (u(beta))(t) - div(vertical bar del u vertical bar(lambda-1) del u) + u(p) were 0 < beta <= lambda < p. For a positive solution of the equation we prove universal bounds and provide blowup rate estimates under suitable assumptions on p < p(0)(lambda, beta, N). In particular, we extend some of the recent results by K. Ammar and Ph. Souplet concerning the blow-up estimates for porous media equations with a source. Our proofs are based on a generalized version of the Bochner-Weitzenbok formula and local energy estimates.

引用

页码：229 / 242

页数：14

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