American Institute of Mathematical Sciences

September  2016, 11(3): 369-393. doi: 10.3934/nhm.2016001

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

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

Received  February 2015 Revised  February 2016 Published  August 2016

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.
Citation: Matthieu Alfaro, Thomas Giletti. Varying the direction of propagation in reaction-diffusion equations in periodic media. Networks & Heterogeneous Media, 2016, 11 (3) : 369-393. doi: 10.3934/nhm.2016001
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