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Point condensation of a model for fungal development. (English. Abridged French version) Zbl 0919.92009

Summary: We study the stationary solutions for a reaction-diffusion system of activator-inhibitor type which arises as a model for fungal development. Under the condition that the activator diffuses slowly and the inhibitor diffuses very quickly we rigorously construct solutions which show single peak patterns near the boundary or in the interior in the activator component and have nearly constant values in the other. We also establish the linear stability and instability of such solutions.

MSC:

92C15 Developmental biology, pattern formation
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
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