ASYMPTOTIC BEHAVIOR FOR A SINGULAR PARABOLIC p-BIHARMONIC EQUATION WITH GRADIENT-TYPE LOGARITHMIC NONLINEARITY

被引：0

作者：

Lv, Jionghao ^{[1
]}

Fang, Zhong-Bo ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年 / 17卷 / 12期

关键词：

Parabolic p- biharmonic equation; logarithmic nonlinearity; singularity coefficient; global existence; blow-up;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the initial boundary value problem for a singular parabolic p- biharmonic equation with gradient-type logarithmic nonlinearity. By the cut-off technique, combined with the methods of Faedo-Galerkin approximation and multiplier, we establish the local solvability. Further, by virtue of the family of potential wells and the modified differential inequality technique, we derive the threshold results of global existence and nonexistence with low initial energy conditions (J(u0) J ( u 0 ) <= d ), the decay property, blow-up with negative initial energy, the estimates of blow-up rate, and the bounds of life span of blow-up solutions with sub critical initial energy. Furthermore, we adopt the Hardy-Sobolev inequality to show the finite time blow-up result with arbitrary initial energy.

引用

页码：3392 / 3419

页数：28