Stability properties for nonlinear diffusion in porous and other media
type: Item
instance of: scholarly article
title: Stability properties for nonlinear diffusion in porous and other media
zbMATH Open document ID: 1027.35054
DOI: 10.1016/S0022-247X(03)00063-5
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: The paper is devoted to the investigation of nonlinear diffusion. A peculiarity of the problem is that the diffusivity is a function of the dependent variable. In particular, the porous medium model can be described in this way, the dependent variable being interpreted as a mass concentration. The equilibrium state is specified by a boundary value problem, and the unsteady state is determined by an initial boundary value problem with the initial value corresponding to an initial perturbation from the steady state. A Lyapunov functional as an integral, positive definite measure of perturbation is introduced and two upper estimates for this functional are obtained, implying global stability of the steady state.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 76R50
zbMATH DE Number: 1956856
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: global stability of the steady state
author: J. N. Flavin
author: S. Rionero
reviewed by: Vyacheslav I. Maksimov
MaRDI profile type: Publication
cites work: Asymptotic and other properties of a nonlinear diffusion model
cites work: The Benard problem for nonlinear heat conduction: unconditional stability
cites work: Nonlinear stability for a thermofluid in a vertical porous slab
cites work: Note on a versatile Liapunov functional: applicability to an elliptic equation
cites work: Q3933378
cites work: DECAY AND OTHER ESTIMATES FOR AN ELASTIC CYLINDER
cites work: Explosive Instabilities in Mechanics
cites work: Q3715482
description: scientific article; zbMATH DE number 1956856