Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model
- Lasarzik, Robert
- Rocca, Elisabetta
- Schimperna, Giulio
2010 Mathematics Subject Classification
- 35D30 35D35 80A22
- Existence of weak solutions, weak-strong uniqueness, phase transition, local solutions
In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in  in two and three dimensions of space. We use a notion of solution inspired by , where the pointwise internal energy balance is replaced by the total energy inequality complemented with a weak form of the entropy inequality. Moreover, we prove existence of local-in-time strong solutions and, finally, we show weak-strong uniqueness of solutions, meaning that every weak solution coincides with a local strong solution emanating from the same initial data, as long as the latter exists.
- Rend. Lincei Mat. Appl., 33 (2022), pp. 229--269, DOI 10.4171/RLM/970 .