Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

Abstract

I prove that the solutions of the phase-field equations, on a subsequence, converge to a weak solution of the Mullins-Sekerka problem with kinetic undercooling. The method is based on energy estimates, a monotonicity formula, and the equipartition of the energy at each time. I also show that for almost all t, the limiting interface is (d - 1)-rectifiable with a square-integrable mean-curvature vector.

Original languageEnglish (US)
Pages (from-to)139-197
Number of pages59
JournalArchive for Rational Mechanics and Analysis
Volume131
Issue number2
DOIs
StatePublished - Jun 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling'. Together they form a unique fingerprint.

Cite this