Exponential time decay of solutions to a nonlinear fourth-order parabolic equation

被引：45
作者：
Jüngel, A
Toscani, G
机构：
[1] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany
[2] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2003年 / 54卷 / 03期
关键词：
asymptotic behavior; entropy dissipation; higher-order parabolic equation; diffusion equation;
D O I：
10.1007/s00033-003-1026-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we investigate the large-time behavior of weak solutions to the nonlinear fourth-order parabolic equation n(t) = -(n(log n)(xx))(xx) modeling interface fluctuations in spin systems. We study here the case x is an element of Omega = (0, 1), with n = 1, n(x) = 0 on partial derivativeOmega. In particular, we prove the exponential decay of u(x, t) towards the constant steady state n(infinity) = 1 in the L-1 norm for long times and we give the explicit rate of decay. The result is based on classical entropy estimates, and on detailed lower bounds for the entropy production.
引用
收藏
页码：377 / 386
页数：10
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