WIAS Preprint No. 2716, (2020)

Further regularity and uniqueness results for a non-isothermal Cahn--Hilliard equation



Authors

  • Ipocoana, Erica
  • Zafferi, Andrea

2010 Mathematics Subject Classification

  • 35Q35 35D35 80A22 35A02 35B65

Keywords

  • Cahn--Hilliard, non-isothermal model, regularity of solutions, uniqueness

DOI

10.20347/WIAS.PREPRINT.2716

Abstract

The aim of this paper is to establish new regularity results for a non-isothermal Cahn--Hilliard system in the two-dimensional setting. The main achievement is a crucial L estimate for the temperature, obtained by a suitable Moser iteration scheme. Our results in particular allow us to get a new simplified version of the uniqueness proof for the considered model.

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