WIAS Preprint No. 2608, (2019)

Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model


Authors

  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Schimperna, Giulio

2010 Mathematics Subject Classification

  • 35D30 35D35 80A22

Keywords

  • Existence of weak solutions, weak-strong uniqueness, phase transition, local solutions

DOI

10.20347/WIAS.PREPRINT.2608

Abstract

In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [26] in two and three dimensions of space. We use a notion of solution inspired by [18], 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.

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