Cabré, X., Coulon, A. and Roquejoffre, J. (2012) Propagation in Fisher-KPP Type Equations with Fractional Diffusion in Periodic Media. Comptes Rendus. Mathématique, 350, 885-890.
https://doi.org/10.1016/j.crma.2012.10.007

has been cited by the following article:

• TITLE: A Singular Limit in a Non-Local Reaction-Diffusion Equation in Periodic Media

  AUTHORS: Yu Wei

  KEYWORDS: Nonlocal Fractional Operator, Exponential Speed of Propagation, Asymptotics

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.12, December 9, 2024

  ABSTRACT: In this paper, we provide an asymptotic analysis of a nonlocal reaction-diffusion equation and with a non-local stable operator of order α∈( 0,1 ) . Firstly, we prove the existence and uniqueness of positive and bounded solutions for the stationary equation. Finally, we perform a long time-long range scaling in order to prove that the stable state invades the unstable state with a speed which is exponential in time.