WIAS Preprint No. 2063, (2015)
Lagrange multiplier and singular limit of double obstacle problems for Allen--Cahn equation with constraint
Authors
- Farshbaf Shaker, Mohammad Hassan
ORCID: 0000-0003-0543-5938 - Fukao, Takeshi
- Yamazaki, Noriaki
2010 Mathematics Subject Classification
- 35K57 35R35 35B25
Keywords
- Allen-Cahn equation, constraint, double obstacle, singular limit, Lagrange multiplier, subdifferential, numerical experiments
DOI
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.
Appeared in
- Math. Methods Appl. Sci., 40 (2017) pp. 5--21.
Download Documents