Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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