Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media

Joachim Escher; Philippe Laurencot; Bogdan-Vasile Matioc

hal-00557791, version 1

Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media

Joachim Escher () ¹, Philippe Laurencot () ², Bogdan-Vasile Matioc () ¹

Annales de l'Institut Henri Poincaré Analyse non linéaire 28 (2011) 583-598

Résumé : We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria.

1 : Institute for Applied Mathematics (IFAM)
Leibniz Universität Hannover
2 : Institut de Mathématiques de Toulouse (IMT)
Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219

hal-00557791, version 1
http://hal.archives-ouvertes.fr/hal-00557791
oai:hal.archives-ouvertes.fr:hal-00557791
Contributeur : Philippe Laurencot <>
Soumis le : Jeudi 20 Janvier 2011, 09:25:39
Dernière modification le : Vendredi 28 Octobre 2011, 08:56:41

Voir la fiche détaillée

Documents associés

PDF :

PS :

arXiv : 1101.3964

DOI : 10.1016/j.anihpc.2011.04.001

Exporter

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Articles dans des revues avec comité de lecture</head>
<biblStruct type="article" xml:id="hal-00557791"><analytic>
<author><persName><forename>Joachim</forename><surname>Escher</surname></persName>
<affiliation>
<orgName type="laboratory">IFAM</orgName>
<orgName type="team">Institute for Applied Mathematics</orgName>
<country>DE</country>
<orgName type="institution">Leibniz Universität Hannover</orgName>
</affiliation>
</author>
<author><persName><forename>Philippe</forename><surname>Laurencot</surname></persName>
<affiliation>
<orgName type="laboratory">IMT</orgName>
<orgName type="team">Institut de Mathématiques de Toulouse</orgName>
<country>FR</country>
<orgName type="institution">Université Paul Sabatier [UPS] - Toulouse III</orgName>
<orgName type="institution">Université Toulouse le Mirail - Toulouse II</orgName>
<orgName type="institution">Université des Sciences Sociales - Toulouse I</orgName>
<orgName type="institution">Institut National des Sciences Appliquées (INSA) - Toulouse</orgName>
<orgName type="institution">CNRS : UMR5219</orgName>
</affiliation>
</author>
<author><persName><forename>Bogdan-Vasile</forename><surname>Matioc</surname></persName>
<affiliation>
<orgName type="laboratory">IFAM</orgName>
<orgName type="team">Institute for Applied Mathematics</orgName>
<country>DE</country>
<orgName type="institution">Leibniz Universität Hannover</orgName>
</affiliation>
</author>
<title type="main" level="a">Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media</title></analytic><monogr><title level="j" type="main">Annales de l'Institut Henri Poincaré Analyse non linéaire</title><imprint><biblScope type="publicationDate">2011-00-00</biblScope><biblScope type="vol">28</biblScope><biblScope type="pp">583-598</biblScope></imprint></monogr><idno type="doi">10.1016/j.anihpc.2011.04.001</idno><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00557791</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00557791/PDF/JEPhLBVM170111.pdf</idno></biblStruct>
</listBibl>
</listBibl>