Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity

被引：7

作者：

Yan, Lijun ^{[1
]}

Yang, Zuodong ^{[2
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Inst Math, Nanjing, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Sch Teacher Educ, Nanjing, Jiangsu, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2018年

基金：

中国国家自然科学基金;

关键词：

Blow-up; Non-extinction; Nonlocal parabolic equation; NEUMANN BOUNDARY-CONDITIONS; SEMILINEAR HEAT-EQUATION; LIOUVILLE-TYPE THEOREMS; P-LAPLACE EQUATION; SUPERLINEAR PROBLEMS; CRITICAL EXPONENTS; SINGULARITY;

D O I：

10.1186/s13661-018-1042-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to studying a nonlocal parabolic equation with logarithmic nonlinearity u log vertical bar u vertical bar - f(Omega) u log vertical bar u vertical bar dx in a bounded domain, subject to homogeneous Neumann boundary value condition. By using the logarithmic Sobolev inequality and energy estimate methods, we get the results under appropriate conditions on blow-up and non-extinction of the solutions, which extend some recent results.

引用

页数：11

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