Finite element approximation of a population spatial adaptation model

Gonzalo Galiano; Julián Velasco

doi:10.3934/mbe.2013.10.637

Article Contents

2013, Volume 10, Issue 3: 637-647. Doi: 10.3934/mbe.2013.10.637

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Finite element approximation of a population spatial adaptation model

Gonzalo Galiano^1, and
Julián Velasco^1,

1.
Dpto. de Matemáticas, Universidad de Oviedo, c/ Calvo Sotelo, 33007-Oviedo

Received: April 30, 2012

Revised: September 30, 2012

Published: March 2013

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Abstract

In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attraction to more favorable environmental regions was included. In this article, we study numerically a modification of their convective term to take account for the notion of spatial adaptation of populations. After describing the model, in which a time non-local drift term is considered, we propose a numerical discretization in terms of a mass-preserving time semi-implicit finite element method. Finally, we provied the results of some biologically inspired numerical experiments showing qualitative differences between the original model of [18] and the model proposed in this article.

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Mathematics Subject Classification: 35K55, 65M60, 92D25.

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References

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