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2011, Volume 2011: 953-962. Doi: 10.3934/proc.2011.2011.953 open access
This issue Previous Article Convergence versus periodicity in a single-loop positive-feedback system 2. Periodic solutions Next Article Continuous maximal regularity and analytic semigroups

Numerical approximation of the Chan-Hillard equation with memory effects in the dynamics of phase separation

  • 1.

    Groupe de Physique de Matériaux UMR CNRS6634, Université de Rouen, 1, Avenue de l'Université, 76801 Saint-Etienne du Rouvray

  • 2.

    Institut für Materialphysik im Weltraum, DLR- Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln

Received:  June 30, 2010
Revised:  April 30, 2011
Published:  August 2017
Abstract Related Papers Cited by
    Abstract
  • We consider the modifi ed Cahn-Hilliard equation for phase separation suggested to account for spinodal decomposition in deeply supercooled binary alloy systems or glasses. This equation contains, as additional term, the second-order time derivative of the concentration multiplied by a positive coefficient $\Tau_d$ (time for relaxation). We consider a numerical approximation scheme based on Fourier spectral method and perform numerical analysis of the scheme. We present results of numerical simulations for three spatial dimensions, and examine the stability and convergence of the scheme.
    Mathematics Subject Classification: Primary: 65M12, 65M22, 68U20; Secondary: 74D10.

    Citation:
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