Cauchy problem for fast diffusion equation with localized reaction

被引：14

作者：

Bai, Xueli ^{[1
]}

Zhou, Shuangshuang ^{[1
]}

Zheng, Sining ^{[1
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Fast diffusion; Localized reaction; Blow-up; Global existence; Fujita exponent; Blow-up rate; Blow-up set; BLOW-UP; PARABOLIC EQUATIONS; CRITICAL EXPONENTS; HEAT-EQUATIONS; GLOBAL-SOLUTIONS; NONEXISTENCE; EXISTENCE; BOUNDARY; THEOREMS;

D O I：

10.1016/j.na.2010.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the Cauchy problem for the fast diffusion equation with a localized reaction. We establish the Fujita type theorem to the problem, and then obtain the diffusion-independent blow-up rate for the non-global solutions. Moreover, we prove that the blow-up set for the problem consists of a single point under large initial data. These conclusions are quite different from those for the slow diffusion case. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2508 / 2514

页数：7

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