| ID | 68320 |
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| Author |
Ninomiya, Hirokazu
School of Interdisciplinary Mathematical Sciences, Meiji University
Taniguchi, Masaharu
Research Institute for Interdisciplinary Science, Okayama University
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| Abstract | Multidimensional traveling front solutions and entire solutions of reaction-diffusion equations have been studied intensively. To study the relationship between multidimensional traveling front solutions and entire solutions, we study the reaction-diffusion equation with a bistable nonlinear term. It is well known that there exist multidimensional traveling front solutions with every speed that is greater than the speed of a one-dimensional traveling front solution connecting two stable equilibria. In this paper, we show that the limit of the n-dimensional multidimensional traveling front solutions as the speeds go to infinity generates an entire solution of the same reaction-diffusion equation in the (n-1)-dimensional space.
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| Note | The version of record of this article, first published in Archive for Rational Mechanics and Analysis, is available online at Publisher’s website: http://dx.doi.org/10.1007/s00205-025-02083-2
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| Published Date | 2025-01-21
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| Publication Title |
Archive for Rational Mechanics and Analysis
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| Volume | volume249
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| Issue | issue1
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| Publisher | Springer Science and Business Media LLC
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| Start Page | 13
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| ISSN | 0003-9527
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| NCID | AA00547035
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| Content Type |
Journal Article
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| language |
English
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| OAI-PMH Set |
岡山大学
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| Copyright Holders | © The Author(s)
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| File Version | publisher
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| Related Url | isVersionOf https://doi.org/10.1007/s00205-025-02083-2
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| License | http://creativecommons.org/licenses/by/4.0/
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| Citation | Ninomiya, H., Taniguchi, M. Traveling Front Solutions of Dimension n Generate Entire Solutions of Dimension (n-1) in Reaction–Diffusion Equations as the Speeds Go to Infinity. Arch Rational Mech Anal 249, 13 (2025). https://doi.org/10.1007/s00205-025-02083-2
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| Funder Name |
Okayama University
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