[Un modèle de chimiotactisme motivé par l'angiogénèse]
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.
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.
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@article{CRMATH_2003__336_2_141_0,
author = {Corrias, L. and Perthame, B. and Zaag, H.},
title = {A chemotaxis model motivated by angiogenesis},
journal = {Comptes Rendus. Math\'ematique},
pages = {141--146},
publisher = {Elsevier},
volume = {336},
number = {2},
year = {2003},
doi = {10.1016/S1631-073X(02)00008-0},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)00008-0/}
}
TY - JOUR AU - Corrias, L. AU - Perthame, B. AU - Zaag, H. TI - A chemotaxis model motivated by angiogenesis JO - Comptes Rendus. Mathématique PY - 2003 SP - 141 EP - 146 VL - 336 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)00008-0/ DO - 10.1016/S1631-073X(02)00008-0 LA - en ID - CRMATH_2003__336_2_141_0 ER -
%0 Journal Article %A Corrias, L. %A Perthame, B. %A Zaag, H. %T A chemotaxis model motivated by angiogenesis %J Comptes Rendus. Mathématique %D 2003 %P 141-146 %V 336 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)00008-0/ %R 10.1016/S1631-073X(02)00008-0 %G en %F CRMATH_2003__336_2_141_0
Corrias, L.; Perthame, B.; Zaag, H. A chemotaxis model motivated by angiogenesis. Comptes Rendus. Mathématique, Tome 336 (2003) no. 2, pp. 141-146. doi : 10.1016/S1631-073X(02)00008-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)00008-0/
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