Time rescaling and asymptotic behavior of some fourth-order degenerate diffusion equations
type: Item
instance of: scholarly article
title: Time rescaling and asymptotic behavior of some fourth-order degenerate diffusion equations
zbMATH Open document ID: 1009.35047
DOI: 10.1016/S0898-1221(01)00316-9
publication date: 2002-08-15T00:00:00Z
review text: The authors investigate the large-time behavior of weak solutions of the degenerate parabolic fourth-order equation \(u'=-(|u|^nu_{xxx})_x\) modeling the evolution of thin films. The main result says that, for all \(n>0\), \(u\) decays exponentially as \(t\to\infty\) towards its mean value \((|\Omega|)^{-1} \int_\Omega u\) (i.e. the limiting stationary state) in the \(L^1\)-norm. Explicit decay rates (depending on \(n\)) are presented.
reviewed by: Grzegorz Karch
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76A20
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1781532
zbMATH Keywords: thin films equations
zbMATH Keywords: exponential decay of solutions
author: José Luis López
author: J. Soler
author: G. Toscani
MaRDI profile type: Publication
cites work: Regularity properties of flows through porous media: The interface
cites work: THE SPREADING OF A THIN DROP BY GRAVITY AND CAPILLARITY
cites work: The Motion with Slip of a Thin Viscous Droplet over a Solid Surface
cites work: Q4214119
cites work: Q4884681
cites work: Higher order nonlinear degenerate parabolic equations
cites work: Source type solutions of a fourth order nonlinear degenerate parabolic equation
cites work: Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
cites work: Q5539510
cites work: Q5529067
cites work: Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations
cites work: Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
cites work: Remarks on entropy and equilibrium states
cites work: Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
cites work: Q3920841
cites work: High-Order Nonlinear Diffusion
cites work: Finite speed of propagation and continuity of the interface for thin viscous flows
cites work: Sharp conditions for 1-dimensional weighted Poincare inequalities
full work available at URL: s0898-1221(01)00316-9
OpenAlex ID: W1967819035
published in: Computers & Mathematics with Applications
Recommended article: Time rescaling and asymptotic behavior of some fourth order degenerate diffusion equations
Recommended article: Q3424400
Recommended article: Asymptotic properties of solutions to fourth-order difference equations on time scales
Recommended article: Q4272250
Recommended article: Long time asymptotics of fourth order parabolic equations
Recommended article: Q3138622
Recommended article: EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATION
Recommended article: Behaviour in time of solutions to a class of fourth order evolution equations
Recommended article: Q3081875
Recommended article: Large time asymptotics for fundamental solutions of diffusion equations
description: scientific article; zbMATH DE number 1781532