Stability of traveling waves of a solute transport equation
type: Item
instance of: scholarly article
title: Stability of traveling waves of a solute transport equation
zbMATH Open document ID: 0884.35011
author: Jack Xin
published in: Journal of Differential Equations
publication date: 1998-04-02T00:00:00Z
review text: The author proves the large time asymptotic stability of traveling wave solutions to the scalar solute transport equation (containment transport equation) with spatially periodic diffusion-adsorption coefficients in one space dimension. The time dependent solutions converge in proper norms to a translate of traveling wave solutions as time approaches infinity. In case of classical traveling waves, the convergence rate is exponential in time for a class of small initial perturbations, and for general order one perturbations, the convergence holds in supremum norm. In case of degenerate Hölder continuous traveling waves, the convergence holds in \(L^1\) norm. As a byproduct, uniqueness up to translation of degenerate traveling waves follows. Maximum principle, \(L^1\) contraction spectral theory, and a space-time invariance property of solutions are used in this article.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 1014439
zbMATH Keywords: \(L^ 1\) contraction spectral theory
zbMATH Keywords: large time asymptotic stability
zbMATH Keywords: spatially periodic diffusion-adsorption coefficients
zbMATH Keywords: uniqueness up to translation
zbMATH Keywords: space-time invariance property
reviewed by: Stanislav Míka
MaRDI profile type: Publication
full work available at URL: jdeq.1996.3228
OpenAlex ID: W2014653737
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DOI: 10.1006/JDEQ.1996.3228
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description: scientific article; zbMATH DE number 1014439