LONG-TIME BEHAVIOR FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS

被引：11

作者：

Li, Hongtao ^{[1
]}

Ma, Shan ^{[2
]}

Zhong, Chengkui ^{[3
]}

机构：

[1] Lanzhou Jiaotong Univ, Sch Traff & Transportat, Lanzhou 730070, Peoples R China

[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[3] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 07期

关键词：

Global solution; global attractor; degenerate parabolic equation; GLOBAL ATTRACTORS; ELLIPTIC-EQUATIONS; GINZBURG-LANDAU; CONVERGENCE; EXISTENCE;

D O I：

10.3934/dcds.2014.34.2873

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The long-time behavior of a class of degenerate parabolic equations in a bounded domain will be considered in the sense that the nonnegative diffusion coefficient a(x) is allowed to vanish on a nonempty closed subset with zero measure. For this purpose, some appropriate weighted Sobolev spaces are introduced and the corresponding embedding theorem is established. Then, we show the global existence and uniqueness of weak solutions. Finally, we distinguish two cases (subcritical and supcritical) to prove the existence of compact attractors for the semigroup associated with this class of equations.

引用

页码：2873 / 2892

页数：20

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