WIAS Preprint No. 2052, (2014)

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


  • Farshbaf Shaker, Mohammad Hassan
    ORCID: 0000-0003-0543-5938
  • Fukao, Takeshi
  • Yamazaki, Noriaki

2010 Mathematics Subject Classification

  • 35K57 35R35 35B25


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




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.

Appeared in

  • Dynamical Systems, Differential Equations and Applications, AIMS Proceedings, 2015, pp. 418--427.

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