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Méléard, S. and Mirrahimi, S. (2015) Singular Limits for Reaction-Diffusion Equations with Fractional Laplacian and Local or Nonlocal Nonlinearity. Communications in Partial Differential Equations, 40, 957-993.
https://doi.org/10.1080/03605302.2014.963606

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.