WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER: DEPENDENCE ON CYLINDER WIDTH.

Jonathan Bell; Chris Cosner

doi:10.1137/0147036

WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER: DEPENDENCE ON CYLINDER WIDTH.

Jonathan Bell, Chris Cosner

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

2 Scopus citations

Abstract

For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.

Original language	English (US)
Pages (from-to)	534-543
Number of pages	10
Journal	SIAM Journal on Applied Mathematics
Volume	47
Issue number	3
DOIs	https://doi.org/10.1137/0147036
State	Published - Jan 1 1987
Externally published	Yes

ASJC Scopus subject areas

Applied Mathematics

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10.1137/0147036

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title = "WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER: DEPENDENCE ON CYLINDER WIDTH.",

abstract = "For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.",

author = "Jonathan Bell and Chris Cosner",

year = "1987",

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AU - Cosner, Chris

PY - 1987/1/1

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N2 - For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.

AB - For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.

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WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER: DEPENDENCE ON CYLINDER WIDTH.

Abstract

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