Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2013-10

AUTHORS

WeiJie Sheng, WanTong Li, ZhiCheng Wang

ABSTRACT

This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle. More... »

PAGES

1969-1982

References to SciGraph publications

Journal

TITLE

Science China Mathematics

ISSUE

10

VOLUME

56

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11425-013-4699-5

DOI

http://dx.doi.org/10.1007/s11425-013-4699-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1032157523


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