SUFFICIENT CONDITIONS FOR NONEXISTENCE OF GRADIENT BLOW-UP FOR NONLINEAR PARABOLIC EQUATIONS

被引：0

作者：

Tersenov, Aris S. ^{[1
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年

关键词：

Bernstein-Nagumo condition; gradient blow-up; a priori estimates nonlinear parabolic equation;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the initial-boundary value problems for nonlinear parabolic equations without Bernstein-Nagumo condition. Sufficient conditions guaranteeing the nonexistence of gradient blow-up are formulated. In particular, we show that for a wide class of nonlinearities the Lipschitz continuity in the space variable together with the strict monotonicity with respect to the solution guarantee that gradient blow-up cannot occur at the boundary or in the interior of the domain.

引用

页数：12

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