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Heterogeneity and strong competition in ecology

Published online by Cambridge University Press:  25 June 2018

H. HUTRIDURGA  and
C. VENKATARAMAN
H. HUTRIDURGA
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK email: h.hutridurga-ramaiah@imperial.ac.uk
C. VENKATARAMAN
Affiliation:
Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9QH, UK email: c.venkataraman@sussex.ac.uk
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Abstract

We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan-type evolution equation with effective coefficients. We also perform some numerical simulations in one and two spatial dimensions that suggest that oscillations in motilities are detrimental to invasion behaviour of a species.

Keywords

HomogenizationEquations in media with periodic structuresAsymptotic analysisStefan problemsFinite element methodsEcology and invasion
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 4 , August 2019 , pp. 682 - 706
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†The research of the first author was supported by the EPSRC programme grant ‘Mathematical fundamentals of Metamaterials for multiscale Physics and Mechanic’ (EP/L024926/1). The second author would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the program ‘Coupling geometric PDEs with physics for cell morphology, motility and pattern formation’ where this project was initiated.

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