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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.

EXISTENCE OF SOLUTIONS FOR A ONE-DIMENSIONAL ALLEN-CAHN EQUATION