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Convergence of the Cahn-Hilliard equation to the Hele-Shaw model

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Abstract

We prove that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of the Hele-Shaw problem under the assumption that classical solutions of the latter exist. The method is based on a new matched asymptotic expansion for solutions, a spectral analysis for linearizd operators, and an estimate for the difference between the true solutions and certain approximate ones.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, 37996-1300, Knoxville, Tennessee

    Nicholas D. Alikakos, Peter W. Bates & Xinfu Chen

  2. Department of Mathematics, Brigham Young University, 84602, Provo, Utah

    Nicholas D. Alikakos, Peter W. Bates & Xinfu Chen

  3. Department of Mathematics and Statistics, University of Pittsburgh, 15260, Pittsburgh, Pennsylvania

    Nicholas D. Alikakos, Peter W. Bates & Xinfu Chen

Authors
  1. Nicholas D. Alikakos
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  2. Peter W. Bates
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  3. Xinfu Chen
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Communicated by D. Kinderlehrer

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Alikakos, N.D., Bates, P.W. & Chen, X. Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Arch. Rational Mech. Anal. 128, 165–205 (1994). https://doi.org/10.1007/BF00375025

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