Global existence and blow-up of weak solutions for a fourth-order parabolic equation with gradient nonlinearity

被引：0

作者：

Zhao, Jinhong ^{[1
]}

Guo, Bin ^{[1
]}

Wang, Jian ^{[2
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

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

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2024年 / 75卷 / 01期

关键词：

Fourth-order parabolic equation; Gradient nonlinearity; Global existence; Blow-up; NAVIER-STOKES EQUATION; SMOOTH SOLUTIONS; SPACES;

D O I：

10.1007/s00033-023-02148-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article deals with the behaviors of solutions to the initial-boundary value problem for a fourth-order parabolic equation with gradient nonlinearity. More precisely, we first get a threshold result for the solutions to exist globally or to blow up in finite time when the initial energy is subcritical and critical, and give an upper bound estimate of the lifespan. Furthermore, we derive the sufficient conditions for the existence of global and blow-up solutions for supercritical initial energy. Finally, we also give a lower bound estimate of the lifespan and obtain some estimates for blow-up rate. These results extend and improve some recent results.

引用

页数：12

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