Asymptotic analysis of a monostable equation in periodic media

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Published: Mar 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.1872

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Matthieu Alfaro
Thomas Giletti

Abstract

We consider a multidimensional monostable reaction-diffusion equation whose nonlinearity involves periodic heterogeneity. This serves as a model of invasion for a population facing spatial heterogeneities. As a rescaling parameter tends to zero, we prove the convergence to a limit interface, whose motion is governed by the minimal speed (in each direction) of the underlying pulsating fronts. This dependance of the speed on the (moving) normal direction is in contrast with the homogeneous case and makes the analysis quite involved. Key ingredients are the recent improvement \cite{A-Gil} %[4]of the well-known spreading properties \cite{Wein02}, %[32], \cite{Ber-Ham-02}, %[9],and the solution of a Hamilton-Jacobi equation.

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How to Cite
Alfaro, M., & Giletti, T. (2016). Asymptotic analysis of a monostable equation in periodic media. Tamkang Journal of Mathematics, 47(1). https://doi.org/10.5556/j.tkjm.47.2016.1872
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Vol. 47 No. 1 (2016)
Section
Special Issue
Author Biographies

Matthieu Alfaro

I3M, Université deMontpellier 2, CC051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France.

Thomas Giletti

IECL, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre-lès-Nancy Cedex, France.

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