Critical Curves of Solutions in Nonlinear Parabolic Equations Involving p, m-Laplace Operators

被引：2

作者：

Liu, Bingchen ^{[1
]}

Zhang, Q. ^{[1
]}

Zhang, X. ^{[1
]}

Zhao, Z. ^{[2
]}

机构：

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[2] Beijing Inst Technol, Sch Informat & Elect, Beijing 100081, Peoples R China

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2018年 / 44卷 / 06期

关键词：

p; m-Laplace equation; Critical global-existence curve; Critical Fujita's curve; Blow-up; BLOW-UP; CRITICAL EXPONENTS;

D O I：

10.1007/s41980-018-0098-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study some nonlinear parabolic equation involving p, m-Laplace operator with nonlinear source and boundary flux. First, we determine the critical curve of the existence of global solutions by constructing self-similar auxiliary functions. Second, the exponent region is proposed where every nontrivial solution blows up in finite time. In addition, blow-up phenomenon of the Fujita type is proved for the corresponding Cauchy problem of the nonlinear parabolic equation.

引用

页码：1427 / 1447

页数：21

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