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dc.contributor.authorIron, Daviden_US
dc.contributor.authorKolokolonikov, Theodoreen_US
dc.contributor.authorRumsey, Johnen_US
dc.contributor.authorWei, Junchengen_US
dc.date.accessioned2013-10-04T18:38:06Z
dc.date.available2013-10-04T18:38:06Z
dc.date.issued2009en_US
dc.identifier.citationIron, David, Theodore Kolokolonikov, John Rumsey, and Juncheng Wei. 2009. "Stability of Curved Interfaces in the Perturbed Two-Dimensional Allen-Cahn System." SIAM Journal on Applied Mathematics 69(5): 1228-16.en_US
dc.identifier.issn00361399en_US
dc.identifier.urihttp://dx.doi.org/10.1137/070706380en_US
dc.identifier.urihttp://hdl.handle.net/10222/37345
dc.description.abstractWe consider the singular limit of a perturbed Allen-Cahn model on a bounded two-dimensional domain: $\left\{\begin{array}{@{}ll@{}} u_t = \varepsilon^2 \Delta u - 2 (u - \varepsilon a) (u^2 - 1), & x \in \Omega \subset \mathbb{R}^2 \ \partial_n u = 0, & x \in \partial \Omega \end{array} \right.$ where $\varepsilon$ is a small parameter and $a$ is an $O(1)$ quantity. We study equilibrium solutions that have the form of a curved interface. Using singular perturbation techniques, we fully characterize the stability of such an equilibrium in terms of a certain geometric eigenvalue problem, and give a simple geometric interpretation of our stability results. Full numerical computations of the time-dependent PDE as well as of the associated two-dimensional eigenvalue problem are shown to be in excellent agreement with the analytical predictions.en_US
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.ispartofSIAM Journal on Applied Mathematicsen_US
dc.titleStability of Curved Interfaces in the Perturbed Two-Dimensional Allen-Cahn Systemen_US
dc.typearticleen_US
dc.identifier.volume69en_US
dc.identifier.issue5en_US
dc.identifier.startpage1228en_US
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