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ID 53604
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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.
Keywords
traveling front
Allen–Cahn equation
nonsymmetric
Note
© 2015 Society for Industrial and Applied Mathematics
Published Date
2015-01
Publication Title
SIAM Journal on Mathematical Analysis
Volume
volume47
Issue
issue1
Publisher
Society for Industrial and Applied Mathematics
Start Page
455
End Page
476
ISSN
0036-1410
NCID
AA00424217
Content Type
Journal Article
Official Url
http://epubs.siam.org/loi/sjmaah
language
英語
Copyright Holders
Society for Industrial and Applied Mathematics
File Version
publisher
Refereed
True
DOI
Web of Science KeyUT