A chemotaxis model motivated by angiogenesis

L. Corrias; B. Perthame; H. Zaag

doi:10.1016/S1631-073X(02)00008-0

Partial Differential Equations

A chemotaxis model motivated by angiogenesis
[Un modèle de chimiotactisme motivé par l'angiogénèse]

Présenté par : Philippe G. Ciarlet

L. Corrias ¹ ; B. Perthame ² ; H. Zaag ²

¹ Département de mathématiques, Université d'Evry Val d'Essonne, rue du Père Jarlan, 91025 Evry cedex, France
² Département de mathématiques et applications, École normale supérieure, et INRIA, projet BANG, 45, rue d'Ulm, 75230 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 141-146.

Abstract (VO)
Résumé

We consider a simple model arising in modeling angiogenesis and more specifically the development of capillary blood vessels due to an exogenous chemo-attractive signal (solid tumors for instance). It is given as coupled system of parabolic equations through a nonlinear transport term. We show that, by opposition to some classical chemotaxis model, this system admits a positive energy. This allows us to develop an existence theory for weak solutions. We also show that, in two dimensions, this system admits a family of self-similar waves.

Nous considérons un modèle simplifié intervenant dans la modélisation de l'angiogénèse et plus précisément le développement de vaisseaux sanguins capillaires sous l'effet d'un signal chemo-attractif exogène (tumeurs solides par exemple). Il s'agit d'un système parabolique couplé par un terme de transport non linéaire. Nous montrons que, contrairement au cas d'autres modèles de chimiotactisme, ce système admet une énergie positive. Ceci nous permet de développer une théorie d'existence de solutions faibles. Nous montrons aussi que, en deux dimensions, ce système admet une famille de solutions autosimilaires.

Reçu le : 2002-11-03
Accepté le : 2002-11-04
Publié le : 2003-01-15

DOI : 10.1016/S1631-073X(02)00008-0

Affiliations des auteurs :

L. Corrias ¹ ; B. Perthame ² ; H. Zaag ²

¹ Département de mathématiques, Université d'Evry Val d'Essonne, rue du Père Jarlan, 91025 Evry cedex, France
² Département de mathématiques et applications, École normale supérieure, et INRIA, projet BANG, 45, rue d'Ulm, 75230 Paris cedex 05, France

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L. Corrias; B. Perthame; H. Zaag. A chemotaxis model motivated by angiogenesis. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 141-146. doi : 10.1016/S1631-073X(02)00008-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)00008-0/

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