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THE MOTION OF WEAKLY INTERACTING LOCALIZED PATTERNS FOR REACTION-DIFFUSION SYSTEMS WITH NONLOCAL EFFECT
| Title: | THE MOTION OF WEAKLY INTERACTING LOCALIZED PATTERNS FOR REACTION-DIFFUSION SYSTEMS WITH NONLOCAL EFFECT |
| Authors: | Ei, Shin-Ichiro Browse this author →KAKEN DB | | Ishii, Hiroshi Browse this author |
| Keywords: | Interaction of pulse solutions | | interaction of front solutions | | nonlocal effect | | convolution | | integral kernel |
| Issue Date: | Jan-2021 |
| Publisher: | American Institute of Mathematical Sciences (AIMS) |
| Journal Title: | Discrete and continuous dynamical systems. Series B |
| Volume: | 26 |
| Issue: | 1 |
| Start Page: | 173 |
| End Page: | 190 |
| Publisher DOI: | 10.3934/dcdsb.2020329 |
| Abstract: | 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. |
| Rights: | 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. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/83744 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 栄 伸一郎
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