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The Cahn-Hilliard Equation with Logarithmic Potentials

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Abstract

Our aim in this article is to discuss recent issues related with the Cahn-Hilliard equation in phase separation with the thermodynamically relevant logarithmic potentials; in particular, we are interested in the well-posedness and the study of the asymptotic behavior of the solutions (and, more precisely, the existence of finite-dimensional attractors). We first consider the usual Neumann boundary conditions and then dynamic boundary conditions which account for the interactions with the walls in confined systems and have recently been proposed by physicists. We also present, in the case of dynamic boundary conditions, some numerical results.

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Authors and Affiliations

  1. Université de La Rochelle, Laboratoire Mathématiques, Image et Applications, Avenue Michel Crépeau, F-17042, La Rochelle Cedex, France

    Laurence Cherfils

  2. Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962, Chasseneuil Futuroscope Cedex, France

    Alain Miranville

  3. Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom

    Sergey Zelik

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  1. Laurence Cherfils
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  2. Alain Miranville
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Lecture held by A. Miranville in the Seminario Matematico e Fisico di Milano on November 29, 2010

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Cherfils, L., Miranville, A. & Zelik, S. The Cahn-Hilliard Equation with Logarithmic Potentials. Milan J. Math. 79, 561–596 (2011). https://doi.org/10.1007/s00032-011-0165-4

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