Author(s)

Yu Wei

School of Mathematics and Statistics, Shandong Normal University, Jinan, China.

In this paper, we provide an asymptotic analysis of a nonlocal reaction-diffusion equation and with a non-local stable operator of order $\alpha \in \left(0,1\right)$ . 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.

Nonlocal Fractional Operator, Exponential Speed of Propagation, Asymptotics

Wei, Y. (2024) A Singular Limit in a Non-Local Reaction-Diffusion Equation in Periodic Media. Journal of Applied Mathematics and Physics, 12, 4057-4076. doi: 10.4236/jamp.2024.1212248.