Periodic solutions of non-isothermal phase separation models with constraint

In this paper, we consider the existence of time periodic solutions to the non-isothermal phase separation models with constraints for the order parameter and the Dirichlet boundary condition for the temperature. We firstly address some approximate problems by the Leray-Schauder fixed point theorem. Then the periodic solutions of the original problem are obtained by establishing some a priori estimates and performing a limiting procedure.