| ID | 53604 |
| FullText URL | |
| Author | |
| Abstract | This paper studies traveling fronts to the Allen–Cahn equation in RN for N ≥ 3. Let
(N −2)-dimensional smooth surfaces be the boundaries of compact sets in RN−1 and assume that all principal curvatures are positive everywhere. We define an equivalence relation between them and prove that there exists a traveling front associated with a given surface and that it is asymptotically stable for given initial perturbation. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.
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| Keywords | traveling front
Allen–Cahn equation
nonsymmetric
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| Note | © 2015 Society for Industrial and Applied Mathematics
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| Published Date | 2015-01
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| Publication Title |
SIAM Journal on Mathematical Analysis
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| Volume | volume47
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| Issue | issue1
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| Publisher | Society for Industrial and Applied Mathematics
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| Start Page | 455
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| End Page | 476
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| ISSN | 0036-1410
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| NCID | AA00424217
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| Content Type |
Journal Article
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| Official Url | http://epubs.siam.org/loi/sjmaah
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| language |
English
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| Copyright Holders | Society for Industrial and Applied Mathematics
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| File Version | publisher
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| Refereed |
True
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| DOI | |
| Web of Science KeyUT |
