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


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.


Weak Solution Energy Inequality Degenerate Parabolic Equation Diffusion Mobility Hilliard Equation 
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© 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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