Uniqueness of weak and entropy solutions

Prove uniqueness for the global-in-time weak and entropy solutions of the subclass of temperature-dependent Cahn–Hilliard equations derived by Miranville and Schimperna.

Background

The paper notes that Marveggio and Schimperna established existence of global-in-time weak and entropy solutions for a subclass of the temperature-dependent Cahn–Hilliard equations derived by Miranville and Schimperna. The paper distinguishes their notion of weak solution from their notion of entropy solution, observing that the former is closer to a classical solution than the latter.

The uniqueness of the solutions in that existing global existence theory is explicitly identified as unknown. This is separate from the paper’s own local unique-solvability result for a more restricted Type I system.