Propagation in a fractional reaction-diffusion equation in a periodically hostile environment

2019/05/13 by Léculier, Alexis, Mirrahimi, Sepideh, Roquejoffre, Jean-Michel
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.04880

Abstract

We provide an asymptotic analysis of a fractional Fisher-KPP type equation in periodic non-connected 1-dimensional media with Dirichlet conditions outside the domain. After demonstrating the existence and uniqueness of a non-trivial bounded stationary state n_+ , we prove that the stable state n_+ invades the unstable state 0 with a speed which is exponential in time.

Related

• A singular limit in a fractional reaction-diffusion equation with periodic coefficients
• Propagation in Fisher-KPP type equations with fractional diffusion in periodic media
• Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations
• The Fisher-KPP equation with nonlinear fractional diffusion
• Front propagation in Fisher-KPP equations with fractional diffusion