Point condensation generated by a reaction-diffusion system in axially symmetric domains

Wei Ming Ni; Izumi Takagi

doi:10.1007/BF03167294

Point condensation generated by a reaction-diffusion system in axially symmetric domains

Wei Ming Ni, Izumi Takagi

Mathematics

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Abstract

In this paper we consider the stationary problem for a reaction-diffusion system of activator-inhibitor type, which models biological pattern formation, in an axially symmetric domain. It is shown that the system has multi-peak stationary solutions such that the activator is localized around some boundary points if the activator diffuses very slowly and the inhibitor diffuses rapidly enough.

Original language	English (US)
Pages (from-to)	327-365
Number of pages	39
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/BF03167294
State	Published - Jun 1 1995

Keywords

point-condensation phenomenon
reaction-diffusion system
semilinear Neumann problem
singular perturbation

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title = "Point condensation generated by a reaction-diffusion system in axially symmetric domains",

abstract = "In this paper we consider the stationary problem for a reaction-diffusion system of activator-inhibitor type, which models biological pattern formation, in an axially symmetric domain. It is shown that the system has multi-peak stationary solutions such that the activator is localized around some boundary points if the activator diffuses very slowly and the inhibitor diffuses rapidly enough.",

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KW - semilinear Neumann problem

KW - singular perturbation

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Point condensation generated by a reaction-diffusion system in axially symmetric domains

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