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- ItemLagrange multiplier and singular limit of double obstacle problems for Allen-Cahn equation with constraint(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Farshbaf Shaker, Mohammad Hassan; Takeshi, Takeshi; Yamazaki, Noriaki; Kenmochi, NobuyukiWe 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.
- ItemSingular limit of Allen-Cahn equation with constraints and its Lagrange multiplier(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Farshbaf Shaker, Mohammad Hassan; Fukao, Takeshi; Yamazaki, NoriakiWe 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.