Singular limit of Allen-Cahn equation with constraints and its Lagrange multiplier

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Date
2014
Volume
2052
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We consider the Allen-Cahn equation with constraint. Our constraint is the subdifferential of the indicator function on the closed interval, which is the multivalued function. In this paper we give the characterization of the Lagrange multiplier to our equation. Moreover, we consider the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier to our problem.

Description
Keywords
Allen-Cahn equation, constraint, double obstacle, singular limit, Lagrange multiplier, subdifferential
Citation
Farshbaf Shaker, M. H., Fukao, T., & Yamazaki, N. (2014). Singular limit of Allen-Cahn equation with constraints and its Lagrange multiplier (Vol. 2052). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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