Rate estimates of gradient blowup for a heat equation with exponential nonlinearity

被引：31

作者：

Zhang, Zhengce ^{[1
]}

Hu, Bei ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Coll Sci, Xian 710049, Peoples R China

[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 12期

关键词：

Gradient blowup; Rate estimate; Nonlinear gradient source; SINGULAR STEADY-STATE; PARABOLIC EQUATIONS; GLOBAL-SOLUTIONS;

D O I：

10.1016/j.na.2010.02.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a one-dimensional semilinear parabolic equation u(t) = u(xx) + e(u)x, for which the spatial derivative of solutions becomes unbounded in finite time while the solutions themselves remain bounded. We establish estimates of blowup rate upper and lower bounds. We prove that in this case the blowup rate does not match the one obtained by the rescaling method. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：4594 / 4601

页数：8

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