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Sharp-interface limit of the Allen-Cahn action functional in one space dimension

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タイトル: Sharp-interface limit of the Allen-Cahn action functional in one space dimension
著者: Kohn, Robert V. 著作を一覧する
Reznikoff, Maria G. 著作を一覧する
Tonegawa, Yoshihiro 著作を一覧する
キーワード: Allen-Cahn equation
stochastic partial diffrential equations
large deviation theory
action minimization
sharp-interface limits
gamma convergence
発行日: 2006年 4月
出版者: Springer
誌名: Calculus of variations and partial differential equations
巻: 25
号: 4
開始ページ: 503
終了ページ: 534
出版社 DOI: 10.1007/s00526-005-0370-5
抄録: We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic arguments and numerical results have suggested that the limiting action should “count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of scaling. In this paper, we prove that for d = 1, the upper bound achieved by the constructions is in fact sharp. Furthermore, we derive a lower bound for the functional itself, which is in agreement with the heuristic picture. To do so, we characterize the sharp-interface limit of the space-time energy measures. The proof relies on an extension of earlier results for the related elliptic problem.
Rights: The original publication is available at www.springerlink.com
Relation (URI): http://www.springerlink.com
資料タイプ: article (author version)
URI: http://hdl.handle.net/2115/8556
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 利根川 吉廣

 

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