The Cahn-Hilliard equation with time-dependent constraint

  • Kubo M
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Abstract

We propose an abstract variational inequality formulation of the Cahn-Hilliard equation with a time-dependent constraint. We introduce notions of strong and weak solutions, and prove that a strong solution, if it exists, is a weak solution, and that the existence of a unique weak solution holds under an appropriate time-dependence condition on the constraint. We also show that the weak solution is a strong solution under appropriate assumptions on the data. Our abstract results can be applied to various concrete problems. © 2012 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Abstract parabolic evolution equations
  • Parabolic variational inequalities
  • Subdifferential operators
  • The Cahn-Hilliard equation

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Authors

  • Masahiro Kubo

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