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

2015/02/01 by Alfaro, Matthieu, Giletti, Thomas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.00209

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 \citeWein02 are actually uniform with respect to the direction.

Related

• Asymptotic analysis of a monostable equation in periodic media
• Reaction-diffusion equations in periodic media: convergence to pulsating fronts
• Spreading speeds for some reaction-diffusion equations with general initial conditions
• Propagating speeds of bistable transition fronts in spatially periodic media
• Front propagation into unstable states for periodic monotone reaction-diffusion systems