We continue to study an initial boundary value problems to a model
describing the evolution in time of diffusive phase interfaces in
sea-ice growth. In a previous paper global existence and the long-time
of behavior of weak solutions in one space was studied under Dirichlet
boundary conditions. Here we show that the global existence of weak
solutions and the long-time behavior are also studied under Neumann
boundary condition. In this paper we study in space dimension lower than
or equal to $3$.