Varying the direction of propagation in reaction-diffusion equations in periodic media

Matthieu  Alfaro; Thomas  Giletti

doi:10.3934/nhm.2016001

Article Contents

2016, Volume 11, Issue 3: 369-393. Doi: 10.3934/nhm.2016001

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Varying the direction of propagation in reaction-diffusion equations in periodic media

Matthieu Alfaro^1, and
Thomas Giletti^2,

1.
IMAG, CC051, Université de Montpellier , 34095 Montpellier
2.
IECL, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre-lès-Nancy Cedex

Received: February 2015

Revised: February 2016

Published online: August 2016

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Abstract

We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed of the underlying pulsating fronts depends continuously on the direction of propagation, and so does its associated profile provided it is unique up to time shifts. We also prove that the spreading properties [25] are actually uniform with respect to the direction.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35B10.

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