  In this paper we consider the Allen-Cahn equation with constraint. In 1994,
Chen and Elliott studied the asymptotic behavior of the solution of the
Allen-Cahn equation with constraint. They proved that the zero level set of the
solution converges to the classical solution of the mean curvature flow under
the suitable conditions on initial data. In 1993, Ilmanen proved the existence
of the mean curvature flow via the Allen-Cahn equation without constraint in
the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation
with constraint.
