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

Institute of Liberal Arts and Sciences

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

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
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
Publication status	Published - 1995 Jun 1

Keywords

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

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

Access to Document

10.1007/BF03167294

Cite this

@article{156d0b73712c4156bd0b3531e7a63779,

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.",

keywords = "point-condensation phenomenon, reaction-diffusion system, semilinear Neumann problem, singular perturbation",

author = "Ni, {Wei Ming} and Izumi Takagi",

year = "1995",

month = jun,

day = "1",

doi = "10.1007/BF03167294",

language = "English",

volume = "12",

pages = "327--365",

journal = "Japan Journal of Industrial and Applied Mathematics",

issn = "0916-7005",

publisher = "Springer Japan",

number = "2",

}

TY - JOUR

T1 - Point condensation generated by a reaction-diffusion system in axially symmetric domains

AU - Ni, Wei Ming

AU - Takagi, Izumi

PY - 1995/6/1

Y1 - 1995/6/1

N2 - 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.

AB - 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.

KW - point-condensation phenomenon

KW - reaction-diffusion system

KW - semilinear Neumann problem

KW - singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=0001672333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001672333&partnerID=8YFLogxK

U2 - 10.1007/BF03167294

DO - 10.1007/BF03167294

M3 - Article

AN - SCOPUS:0001672333

SN - 0916-7005

VL - 12

SP - 327

EP - 365

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this