open access

https://hdl.handle.net/2115/83744

THE MOTION OF WEAKLY INTERACTING LOCALIZED PATTERNS FOR REACTION-DIFFUSION SYSTEMS WITH NONLOCAL EFFECT

英語

integral kernel

2021-01

American Institute of Mathematical Sciences (AIMS)

Discrete and continuous dynamical systems. Series B

26(1)

173-190

In this paper, we analyze the interaction of localized patterns such as traveling wave solutions for reaction-diffusion systems with nonlocal effect in one space dimension. We consider the case that a nonlocal effect is given by the convolution with a suitable integral kernel. At first, we deduce the equation describing the movement of interacting localized patterns in a mathematically rigorous way, assuming that there exists a linearly stable localized solution for general reaction-diffusion systems with nonlocal effect. When the distances between localized patterns are sufficiently large, the motion of localized patterns can be reduced to the equation for the distances between them. Finally, using this equation, we analyze the interaction of front solutions to some nonlocal scalar equation. Under some assumptions, we can show that the front solutions are interacting attractively for a large class of integral kernels.

学術雑誌論文

Accepted Manuscript

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and continuous dynamical systems. Series B following peer review. The definitive publisher-authenticated version January 2021,26(1): 173-190. is available online at:http://www.aimsciences.org/article/doi/10.3934/dcdsb.2020329.

1531-3492