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
收藏
页码：1161 / 1175
页数：15
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