A singular Gierer-Meinhardt system with different source terms

Marius Ghergu (1, 2) , Vicentiu Radulescu (1)

1 UCV - Department of Mathematics
2 IMAR - "Simion Stoilow" Institute of Mathematics

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.

Mots clés: Gierer-Meinhardt; nonlinear elliptic system; morphogenesis; activator-inhibitor; maximum principle

Domaines: Equations aux dérivées partielles [math.AP]

Marius Ghergu, Vicentiu Radulescu. A singular Gierer-Meinhardt system with different source terms. 2006. ⟨hal-00116341⟩