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Archive for Rational Mechanics and Analysis

, Volume 219, Issue 3, pp 1161–1184 | Cite as

Weak Solutions for the Cahn–Hilliard Equation with Degenerate Mobility

  • Shibin DaiEmail author
  • Qiang Du
Article

Abstract

In this paper, we study the well-posedness of Cahn–Hilliard equations with degenerate phase-dependent diffusion mobility. We consider a popular form of the equations which has been used in phase field simulations of phase separation and microstructure evolution in binary systems. We define a notion of weak solutions for the nonlinear equation. The existence of such solutions is obtained by considering the limits of Cahn–Hilliard equations with non-degenerate mobilities.

Keywords

Weak Solution Energy Inequality Degenerate Parabolic Equation Diffusion Mobility Hilliard 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA

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