On a class of singular Gierer–Meinhardt systems arising in morphogenesis

Marius Ghergu; Vicenţiu Rădulescu

doi:10.1016/j.crma.2006.12.008

Partial Differential Equations

On a class of singular Gierer–Meinhardt systems arising in morphogenesis
[Sur une classe de systèmes singuliers de Gierer–Meinhardt avec applications en morphogenèse]

Présenté par : Philippe G. Ciarlet

Marius Ghergu ¹ ; Vicenţiu Rădulescu ²

¹ Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
² Department of Mathematics, University of Craiova, RO-200585 Craiova, Romania

Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 163-168.

Résumé
Abstract

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.

Reçu le : 2006-11-26
Accepté le : 2006-12-02
Publié le : 2007-01-16

DOI : 10.1016/j.crma.2006.12.008

Affiliations des auteurs :

Marius Ghergu ¹ ; Vicenţiu Rădulescu ²

¹ Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
² Department of Mathematics, University of Craiova, RO-200585 Craiova, Romania

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     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},
}

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Marius Ghergu; Vicenţiu Rădulescu. On a class of singular Gierer–Meinhardt systems arising in morphogenesis. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 163-168. doi : 10.1016/j.crma.2006.12.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.12.008/

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