Long-time behavior for a nonlinear fourth-order parabolic equation

被引：36

作者：

Cáceres, MJ

Carrillo, JA

Toscani, G

机构：

[1] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

[2] Univ Autonoma Barcelona, ICREA, E-08193 Bellaterra, Spain

[3] Univ Autonoma Barcelona, Dept Matemat, E-08193 Bellaterra, Spain

[4] Univ Pavia, Dept Math, I-27100 Pavia, Italy

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 03期

关键词：

asymptotic behavior; entropy dissipation; degenerate parabolic equation; diffusion equation;

D O I：

10.1090/S0002-9947-04-03528-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution.

引用

页码：1161 / 1175

页数：15

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