A generalization of the Allen-Cahn equation
نویسندگان
چکیده
منابع مشابه
A Generalization of the Allen-cahn Equation
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 ...
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We consider the Allen-Cahn equation ε∆u + u− u = 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R such that the mean curvature is positive at each boundary point. We show that there exists a sequence εj → 0 such that the Allen-Cahn equation has a solution uεj with an interface which approaches the boundary as j → +∞.
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Keywords: Allen–Cahn equation Finite element method Operator splitting method Unconditionally stable scheme a b s t r a c t We present an unconditionally stable hybrid finite element method for solving the Allen– Cahn equation, which describes the temporal evolution of a non-conserved phase-field during the antiphase domain coarsening in a binary mixture. Its various modified forms have been ap...
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ژورنال
عنوان ژورنال: IMA Journal of Applied Mathematics
سال: 2013
ISSN: 0272-4960,1464-3634
DOI: 10.1093/imamat/hxt044