An application of homogenization techniques to population dynamics models
B. E. Ainseba W. E. Fitzgibbon M. Langlais J. J. Morgan
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.
keywords: predator-prey. Spatial heterogeneities homogenized model cat retrovirus and persistence reaction advection diffusion equations
A reaction-diffusion system modeling direct and indirect transmission of diseases
W. E. Fitzgibbon M. Langlais J.J. Morgan
We study the global existence and approximation of the solutions to a reaction diffusion system coupled with an ordinary differential equation modeling direct transmission between individuals and indirect transmission via a contaminated environment of an epidemic disease.
keywords: Reaction diffusion equations global existence.

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