Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

被引：0

作者：

J. A. Carrillo

G. Toscani

机构：

[1] Departamento de Matemática Aplicada,

[2] Universidad de Granada,undefined

[3] 18071 Granada,undefined

[4] Spain,undefined

[5] Department of Mathematics,undefined

[6] University of Pavia,undefined

[7] via Ferrata 1,undefined

[8] 27100 Pavia,undefined

[9] Italy,undefined

来源：

Communications in Mathematical Physics | 2002年 / 225卷

关键词：

Entropy; Porous Medium; Time Decay; Parabolic Equation; Fourth Order;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation ut=−(uuxxx)x, modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u0(x)∈H1(ℝ), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L1-norm of the strong solution u(x,t) towards the unique (among source type solutions) strong source type solution of the equation with the same mass. The method we use is based on the study of the time decay of the entropy introduced in [13] for the porous medium equation, and uses analogies between the thin film equation and the porous medium equation.

引用

页码：551 / 571

页数：20