Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Convergence to equilibrium for a second-order time semi-discretization ofthe Cahn-Hilliard equation

1 MOX– Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica,Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
2 Laboratoire Paul Painlevé, U.M.R. CNRS 8524, Université Lille 1, Cité Scientifique, F-59655 Villeneuve d’Ascq Cedex, France
3 Team RAPSODI, Inria Lille - Nord Europe, 40 av. Halley, F-59650 Villeneuve d’Ascq, France
4 Laboratoire de Mathématiques et Applications, Université de Poitiers, CNRS, F-86962 Chasseneuil, France

Special Issues: Nonlinear Evolution PDEs, Interfaces and Applications

We consider a second-order two-step time semi-discretization of the Cahn-Hilliard equation with an analytic nonlinearity. The time-step is chosen small enough so that the pseudo-energy associated withdiscretization is nonincreasing at every time iteration. We prove that the sequence generated by the scheme converges to a steady state as time tends to infinity. We also obtain convergence rates in the energy norm. The proof is based on the Łojasiewicz-Simon inequality.
  Article Metrics
Download full text in PDF

Export Citation

Article outline

Copyright © AIMS Press All Rights Reserved