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.
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页码：377 / 386
页数：10
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