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.
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页数：11
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