[Sur une classe de systèmes singuliers de Gierer–Meinhardt avec applications en morphogenèse]
On étudie l'existence ou la non-existence des solutions classiques pour une classe de systèmes singuliers de Gierer–Meinhardt avec condition de Dirichlet sur le bord. La caractéristique de notre modèle réside dans la présence de sources différentes pour l'activateur et aussi pour l'inhibiteur. Des propriétés supplémentaires de régularité et d'unicité sont établies en dimension 1.
We study the existence or the nonexistence of classical solutions to a singular Gierer–Meinhardt system with Dirichlet boundary condition. The main feature of our model is that the activator and the inhibitor have different sources given by general nonlinearities. Additional regularity and uniqueness results are established for the one-dimensional case.
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@article{CRMATH_2007__344_3_163_0,
author = {Ghergu, Marius and R\u{a}dulescu, Vicen\c{t}iu},
title = {On a class of singular {Gierer{\textendash}Meinhardt} systems arising in morphogenesis},
journal = {Comptes Rendus. Math\'ematique},
pages = {163--168},
publisher = {Elsevier},
volume = {344},
number = {3},
year = {2007},
doi = {10.1016/j.crma.2006.12.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.12.008/}
}
TY - JOUR AU - Ghergu, Marius AU - Rădulescu, Vicenţiu TI - On a class of singular Gierer–Meinhardt systems arising in morphogenesis JO - Comptes Rendus. Mathématique PY - 2007 SP - 163 EP - 168 VL - 344 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.12.008/ DO - 10.1016/j.crma.2006.12.008 LA - en ID - CRMATH_2007__344_3_163_0 ER -
%0 Journal Article %A Ghergu, Marius %A Rădulescu, Vicenţiu %T On a class of singular Gierer–Meinhardt systems arising in morphogenesis %J Comptes Rendus. Mathématique %D 2007 %P 163-168 %V 344 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.12.008/ %R 10.1016/j.crma.2006.12.008 %G en %F CRMATH_2007__344_3_163_0
Ghergu, Marius; Rădulescu, Vicenţiu. On a class of singular Gierer–Meinhardt systems arising in morphogenesis. Comptes Rendus. Mathématique, Tome 344 (2007) no. 3, pp. 163-168. doi : 10.1016/j.crma.2006.12.008. http://www.numdam.org/articles/10.1016/j.crma.2006.12.008/
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