A Generalization of the Allen-cahn Equation
نویسندگان
چکیده
Our aim in this paper is to study generalizations of the Allen-Cahn equation based on a modification of the Ginzburg-Landau free energy proposed in [25]. In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen-Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
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