Non-linear-System for Non-isothermal Diffusive Phase Separation

An evolution system, which extends the Cahn-Hilliard model to non-isothermal situations subject to convex constraints for solutions, is studied. The problem can be considered as representing a simple model of non-isothermal phase separation driven by diffusive mechanisms. A variational formulation of the problem is introduced, using t-dependent subdifferential operator techniques in Hilbert spaces. Existence and uniqueness of weak solutions are proved.