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Volume 3, Number 3, 2013, Pages 265-277                                                                DOI:10.11948/2013019
Existence Of Solutions For A One-Dimensional Allen-Cahn Equation
Alain Miranville
Keywords:Allen-Cahn equation
Abstract:
      Our aim in this paper is to prove the existence and uniqueness of solutionsfor a one-dimensional Allen-Cahn type equation based on a modication of the Ginzburg-Landau free energy proposed in [9]. In particular, the free energy contains an additionalterm called Willmore regularization and takes into account anisotropy eects.
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