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Journal of Mathematical Sciences

, Volume 189, Issue 4, pp 604–636 | Cite as

A Variational Approach to a Cahn–Hilliard Model in a Domain with Nonpermeable Walls

  • L. Cherfils
  • S. Gatti
  • A. Miranville
Article

We deal with the well-posedness and the long time behavior of a Cahn–Hilliard model with a singular bulk potential and suitable dynamic boundary conditions. We assume that the system is confined in a vessel with nonpermeable walls and the total mass, in the bulk and on the boundary, is conserved. As a result, the well-posedness in the sense of distributions may not hold and new notions of solutions are required. The same problem has been analyzed, relying on duality techniques, under weak assumptions on the nonlinearities. We improve these results by introducing a variational formulation of the problem, based on a proper variational inequality. Bibliography: 26 titles.

Keywords

Global Attractor Variational Solution Singular Function Singular Potential Porous Media Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Université de La Rochelle, Laboratoire MIALa Rochelle CedexFrance
  2. 2.Università di Modena e Reggio EmiliaModenaItaly
  3. 3.Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MIFuturoscope Chasseneuil CedexFrance

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