Global existence and exponential growth of solution for the logarithmic Boussinesq-type equation
Global existence and exponential growth of solution for the logarithmic Boussinesq-type equation
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DOI：
10.1016/j.jmaa.2015.11.082
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发表时间：
2016-04
影响因子：
1.3
通讯作者：
Qingying Hu;Hongwei Zhang;Gongwei Liu
中科院分区：
文献类型：
--
作者：
Qingying Hu;Hongwei Zhang;Gongwei Liu
本文研究了一类带对数非线性项的Boussinesq型方程的初边值问题。利用势阱方法结合对数Sobolev不等式，得到了整体解的存在性。最后证明了在适当的初值条件下，解的L2范数将随着时间的无穷大而指数增长。结果表明，多项式非线性是Boussinesq方程解在有限时间爆破的临界条件。
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.