双调和方程
数学
数学分析
对数
非线性系统
抛物型偏微分方程
Dirichlet边界条件
乘数(经济学)
边值问题
偏微分方程
物理
量子力学
经济
宏观经济学
作者
Zhiqing Liu,Zhong Bo Fang
标识
DOI:10.1016/j.nonrwa.2022.103780
摘要
This paper is concerned with the well-posedness and asymptotic behavior of Dirichlet initial boundary value problem for a singular parabolic p-biharmonic equation with logarithmic nonlinearity. We establish the local solvability by the technique of cut-off combining with the methods of Faedo–Galerkin approximation and multiplier. Meantime, by virtue of the family of potential wells, we use the technique of modified differential inequality and improved logarithmic Sobolev inequality to obtain the global solvability, infinite and finite time blow-up phenomena, and derive the upper bound of blow-up time as well as the estimate of blow-up rate. Furthermore, the results of blow-up with arbitrary initial energy and extinction phenomena are presented.
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