Applications of Mathematics

, Volume 54, Issue 2, pp 89–115 | Cite as

On the Caginalp system with dynamic boundary conditions and singular potentials

  • L. CherfilsEmail author
  • A. Miranville


This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in H 2, the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Lojasiewicz inequality in order to prove the convergence of solutions to steady states.


Caginalp phase field system singular potential dynamic boundary conditions global existence global attractor Łojasiewicz-Simon inequality convergence to a steady state 

MSC 2000

35B40 35B41 80A22 


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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2009

Authors and Affiliations

  1. 1.Université de La Rochelle, LMALa Rochelle CedexFrance
  2. 2.Université de PoitiersFuturoscope Chasseneuil CedexFrance

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