Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:422

Article

Chen, Hua¹  Luo, Peng¹  Liu, Gongwei² 

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Henan Univ Technol, Dept Math, Zhengzhou 450052, Peoples R China

关键词: Global solution;    Blow-up;    Logarithmic nonlinearity;    Potential wells;   

DOI  :  10.1016/j.jmaa.2014.08.030

来源: Elsevier

【 摘 要 】

We study the initial boundary value problem of a semilinear heat equation with logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, we obtain the existence of global solution and blow-up at +infinity under some suitable conditions. On the other hand, the results for decay estimates of the global solutions are also given. Our result in this paper means that the polynomial nonlinearity is a critical condition of blow-up in finite time for the solutions of semilinear heat equations. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free