Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media
type: Item
instance of: scholarly article
title: Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media
zbMATH Open document ID: 0819.76097
DOI: 10.1007/BF00380794
author: Jack Xin
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-08-27T00:00:00Z
review text: We prove the existence of multidimensional traveling-wave solutions to the scalar equation for the transport of solutes (contaminants) with nonlinear adsorption and spatially periodic convection-diffusion- adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the Lax and Oleinik entropy conditions. In the nondegenerate case, we also prove the uniqueness of the traveling waves. We use the sliding domain method, the continuation method, spectral theory, maximum principles, and a priori estimates. In the degenerate case, the traveling waves are weak solutions of a degenerate parabolic equation and are only Hölder continuous. We obtain them by taking suitable limits on the nondegenerate traveling waves.
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 754024
zbMATH Keywords: nonlinear adsorption
zbMATH Keywords: periodic convection-diffusion-adsorption coefficients
zbMATH Keywords: Lax and Oleinik entropy conditions
zbMATH Keywords: nondegenerate case
zbMATH Keywords: sliding domain method
zbMATH Keywords: continuation method
zbMATH Keywords: spectral theory
zbMATH Keywords: maximum principles
zbMATH Keywords: a priori estimates
zbMATH Keywords: degenerate case
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 754024