Stability of perturbed nonlinear parabolic equations with Sturmian property
type: Item
instance of: scholarly article
title: Stability of perturbed nonlinear parabolic equations with Sturmian property
zbMATH Open document ID: 1061.35017
author: M. Chaves
author: V. A. Galaktionov
published in: Journal of Functional Analysis
publication date: 2004-11-23T00:00:00Z
review text: In an abstract setting, the authors study the stability of an equilibrium \(f^*\) of an autonomous dynamical system under asymptotically small perturbations of \(f^*\), and show that such stability takes place if the domain of attraction for \(f^*\) contains a one-parameter ordered family (see the paper for details and the corresponding order relation). In the stability analysis they make use of a so-called \(S\)-relation inherited from the Sturmian zero set properties for linear parabolic equations. As application they show stability of the self-similar blow-up behavior for the porous medium equation, the \(p\)-Laplacian equation and the dual porous medium equation in \({\mathbb R}\) with nonlinear lower-order perturbation.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 2117855
zbMATH Keywords: quasilinear parablic equation
zbMATH Keywords: nonautonomous perturbation
zbMATH Keywords: blow-up self-similarity
zbMATH Keywords: porous medium equation
zbMATH Keywords: \(p\)-Laplacian equation
zbMATH Keywords: dual porous medium equation
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
full work available at URL: j.jfa.2004.03.007
OpenAlex ID: W2058497356
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DOI: 10.1016/J.JFA.2004.03.007
description: scientific article; zbMATH DE number 2117855