WELL-POSEDNESS AND LONG-TIME BEHAVIOUR FOR THE NON-ISOTHERMAL CAHN-HILLIARD EQUATION WITH MEMORY

摘要

In this paper we study a temperature dependent phase field model with memory. The case where both the equation for the temperature and that for the order parameter is of fractional time order is covered. Under physically reasonable conditions on the nonlinearities we prove global well-posedness in the L_p setting and show that each solution converges to a steady state as time goes to infinity.