Premium
Lagrange multiplier and singular limit of double obstacle problems for the Allen–Cahn equation with constraint
Author(s) -
FarshbafShaker Mohammad Hassan,
Fukao Takeshi,
Yamazaki Noriaki
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3905
Subject(s) - mathematics , lagrange multiplier , neumann boundary condition , mathematical analysis , boundary value problem , obstacle problem , constraint algorithm , boundary (topology) , multiplier (economics) , free boundary problem , limit (mathematics) , obstacle , laplace's equation , mathematical optimization , law , political science , economics , macroeconomics
We study the properties of the Lagrange multiplier for an Allen–Cahn equation with a double obstacle potential. Here, the dynamic boundary condition, including the Laplace–Beltrami operator on the boundary, is investigated. We then establish the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier of our problem. We present remarks on a trace problem as well as on the Neumann boundary condition. Moreover, we describe a numerical experiment for a problem with Neumann boundary condition using the Lagrange multiplier. Copyright © 2016 John Wiley & Sons, Ltd.