start-ver=1.4
cd-journal=joma
no-vol=47
cd-vols=
no-issue=1
article-no=
start-page=455
end-page=476
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2015
dt-pub=201501
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=An (N-1)-dimensional convex compact set gives an N-dimensional traveling front in the Allen--Cahn equation
en-subtitle=
kn-subtitle=
en-abstract=
kn-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.
en-copyright=
kn-copyright=

en-aut-name=TaniguchiMasaharu
en-aut-sei=Taniguchi
en-aut-mei=Masaharu
kn-aut-name=谷口雅治
kn-aut-sei=谷口
kn-aut-mei=雅治
aut-affil-num=1
ORCID=

affil-num=1
en-affil=
kn-affil=自然科学研究科
en-keyword=traveling front
kn-keyword=traveling front
en-keyword=Allen–Cahn equation
kn-keyword=Allen–Cahn equation
en-keyword=nonsymmetric
kn-keyword=nonsymmetric
END