WIAS Preprint No. 2063, (2015)

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


  • Farshbaf Shaker, Mohammad Hassan
  • Fukao, Takeshi
  • Yamazaki, Noriaki

2010 Mathematics Subject Classification

  • 35K57 35R35 35B25


  • Allen-Cahn equation, constraint, double obstacle, singular limit, Lagrange multiplier, subdifferential, numerical experiments




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.

Appeared in

  • Math. Methods Appl. Sci., 40 (2017) pp. 5--21.

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