Global existence for semilinear reaction-diffusion systems on evolving domains

Chandrasekhar Venkataraman; Omar Lakkis; Anotida Madzvamuse

doi:10.1007/s00285-011-0404-x

Global existence for semilinear reaction-diffusion systems on evolving domains

Chandrasekhar Venkataraman^*, Omar Lakkis, Anotida Madzvamuse

^*Corresponding author for this work

Applied Mathematics

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

Abstract

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.

Original language	English
Pages (from-to)	41-67
Number of pages	27
Journal	Journal of Mathematical Biology
Volume	64
Issue number	1-2
DOIs	https://doi.org/10.1007/s00285-011-0404-x
Publication status	Published - Jan 2012

Keywords

Reaction-diffusion systems
Global existence
Evolving domains
Biological pattern formation
GROWING DOMAINS
PATTERN-FORMATION
MODEL

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10.1007/s00285-011-0404-x

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title = "Global existence for semilinear reaction-diffusion systems on evolving domains",

abstract = "We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.",

keywords = "Reaction-diffusion systems, Global existence, Evolving domains, Biological pattern formation, GROWING DOMAINS, PATTERN-FORMATION, MODEL",

author = "Chandrasekhar Venkataraman and Omar Lakkis and Anotida Madzvamuse",

year = "2012",

month = jan,

doi = "10.1007/s00285-011-0404-x",

language = "English",

volume = "64",

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T1 - Global existence for semilinear reaction-diffusion systems on evolving domains

AU - Venkataraman, Chandrasekhar

AU - Lakkis, Omar

AU - Madzvamuse, Anotida

PY - 2012/1

Y1 - 2012/1

N2 - We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.

AB - We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.

KW - Reaction-diffusion systems

KW - Global existence

KW - Evolving domains

KW - Biological pattern formation

KW - GROWING DOMAINS

KW - PATTERN-FORMATION

KW - MODEL

U2 - 10.1007/s00285-011-0404-x

DO - 10.1007/s00285-011-0404-x

M3 - Article

SN - 0303-6812

VL - 64

SP - 41

EP - 67

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 1-2

ER -

Global existence for semilinear reaction-diffusion systems on evolving domains

Abstract

Keywords

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