Lagrange multiplier and singular limit of double obstacle problems for Allen-Cahn equation with constraint

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Date
2015
Volume
2063
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We consider an Allen--Cahn equation with a constraint of double obstacle-type. This constraint is a subdifferential of an indicator function on the closed interval, which is a multivalued function. In this paper we study the properties of the Lagrange multiplier to our equation. Also, we consider the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier to our double obstacle problem. Moreover, we give some numerical experiments of our problem by using the Lagrange multiplier.

Description
Keywords
Allen-Cahn equation, constraint, double obstacle, singular limit, Lagrange multiplier, subdifferential, numerical experiments
Citation
Farshbaf Shaker, M. H., Takeshi, T., Yamazaki, N., & Kenmochi, N. (2015). Lagrange multiplier and singular limit of double obstacle problems for Allen-Cahn equation with constraint (Vol. 2063). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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