Some analytical results on the Gray-Scott model

F. Dkhil; E. Logak; Y. Nishiura

Some analytical results on the Gray-Scott model

F. Dkhil, E. Logak, Y. Nishiura

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

Abstract

We consider the Gray-Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to exist near the equal diffusivities and equal transformation rates case. We also provide numerical simulations illustrating our results.

Original language	English
Pages (from-to)	225-261
Number of pages	37
Journal	Asymptotic Analysis
Volume	39
Issue number	3-4
Publication status	Published - 2004 Dec 1
Externally published	Yes

Keywords

Autocatalysis
Gray-Scott model
Reaction-diffusion system
Self-replicating patterns
Travelling front
Travelling pulse

ASJC Scopus subject areas

Mathematics(all)

Cite this

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abstract = "We consider the Gray-Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to exist near the equal diffusivities and equal transformation rates case. We also provide numerical simulations illustrating our results.",

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AU - Nishiura, Y.

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N2 - We consider the Gray-Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to exist near the equal diffusivities and equal transformation rates case. We also provide numerical simulations illustrating our results.

AB - We consider the Gray-Scott model for cubic autocatalysis. We prove nonexistence results on stationary and travelling pulse solutions for some domain of parameters. We obtain an explicit travelling front in the one dimensional case for equal diffusivities and equal transformation rates of the reactants. We prove that travelling fronts continue to exist near the equal diffusivities and equal transformation rates case. We also provide numerical simulations illustrating our results.

KW - Autocatalysis

KW - Gray-Scott model

KW - Reaction-diffusion system

KW - Self-replicating patterns

KW - Travelling front

KW - Travelling pulse

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JO - Asymptotic Analysis

JF - Asymptotic Analysis

IS - 3-4

ER -

Some analytical results on the Gray-Scott model

Abstract

Keywords

ASJC Scopus subject areas

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