Global existence and exponential growth of solution for the logarithmic Boussinesq-type equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:436

Article

Hu, Qingying¹  Zhang, Hongwei¹  Liu, Gongwei¹ 

[1] Henan Univ Technol, Dept Math, Zhengzhou 450001, Peoples R China

关键词: Logarithmic Boussinesq-type equation;    Initial boundary value problem;    Existence of global solution;    Exponential growth;   

DOI  :  10.1016/j.jmaa.2015.11.082

来源: Elsevier

【 摘 要 】

In this paper we consider the Boussinesq-type equation associated with logarithmic nonlinear term and initial boundary value conditions. By using potential well method combined with the logarithmic Sobolev inequality, we obtain the existence of global solution. At last we show that the L-2-norm of the solution will grow up as an exponential function as time goes to infinity under some suitable conditions for initial data. The result shows that the polynomial nonlinearity is a critical condition of blow-up in finite time for the solutions of Boussinesq equations. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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