On the second inner variations of Allen–Cahn type energies and applications to local minimizers
نویسنده
چکیده
Article history: Received 18 September 2014 Available online 4 November 2014 MSC: 49A50 49J45 58E12
منابع مشابه
On the Second Inner Variation of the Allen-Cahn Functional and Its Applications
In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the singlemultiplicity property of the limiting energy, that the Morse indic...
متن کاملSlow motion for the nonlocal Allen–Cahn equation in n-dimensions
The goal of this paper is to study the slow motion of solutions of the nonlocal Allen–Cahn equation in a bounded domain Ω ⊂ R, for n > 1. The initial data is assumed to be close to a configuration whose interface separating the states minimizes the surface area (or perimeter); both local and global perimeter minimizers are taken into account. The evolution of interfaces on a time scale ε−1 is d...
متن کاملPrimal-dual active set methods for Allen-Cahn variational inequalities
This thesis aims to introduce and analyse a primal-dual active set strategy for solving Allen-Cahn variational inequalities. We consider the standard Allen-Cahn equation with non-local constraints and a vector-valued Allen-Cahn equation with and without non-local constraints. Existence and uniqueness results are derived in a formulation involving Lagrange multipliers for local and non-local con...
متن کاملThe existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0
متن کاملFront Propagation in Geometric and Phase Field Models of Stratified Media
We study front propagation problems for forced mean curvature flows and their phase field variants that take place in stratified media, that is, heterogeneous media whose characteristics do not vary in one direction.We consider phase change fronts in infinite cylinders whose axis coincides with the symmetry axis of the medium. Using the recently developed variational approaches, we provide a co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015