An application of homogenization techniques to population dynamics models

B. E. Ainseba; W. E. Fitzgibbon; M. Langlais; J. J. Morgan

doi:10.3934/cpaa.2002.1.19

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2002, Volume 1, Issue 1: 19-33. Doi: 10.3934/cpaa.2002.1.19

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An application of homogenization techniques to population dynamics models

1.
Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, case 26, U.F.R. Sciences et Modélisation, Université Victor Segalen Bordeaux 2,33076 Bordeaux Cedex
2.
Department of Mathematics, University of Houston, Houston, Texas, 77204-3476
3.
Department of Mathematics, Texas A & M University, College Station, Texas, 77843-3368

Received: July 2001

Published: March 2002

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Abstract

We are interested in partial differential equations and systems of partial differential equations arising in some population dynamics models, for populations living in heterogeneous spatial domains. Discontinuities appear in the coefficients of divergence form operators and in reaction terms as well. Global posedness results are given. For models offering a great a degree of heterogeneity we derive simpler models with constant coefficients by applying homogenization method. Long term behavior is then analyzed.

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Mathematics Subject Classification: 35K57, 35R05, 35B27, 92D25, 92D30.

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