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Maximal Lp-regularity and Long-time Behaviour of the Non-isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions

  • Jan Prüss
  • Mathias Wilke
Part of the Operator Theory: Advances and Applications book series (OT, volume 168)

Abstract

In this paper we investigate the nonlinear Cahn-Hilliard equation with nonconstant temperature and dynamic boundary conditions. We show maximal L p-regularity for this problem with inhomogeneous boundary data. Furthermore we show global existence and use the Lojasiewicz-Simon inequality to show that each solution converges to a steady state as time tends to infinity, as soon as the potential Φ and the latent heat λ satisfy certain growth conditions.

Keywords

Conserved phase field models Cahn-Hilliard equation dynamic boundary condition maximal regularity Lojasiewicz-Simon inequality convergence to steady states 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Jan Prüss
    • 1
  • Mathias Wilke
    • 1
  1. 1.Fachbereich Mathematik und InformatikMartin-Luther-Universität Halle-WittenbergHalleGermany

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