SeminarsStability of curved interfaces in the perturbed Allen-Cahn model
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The perturbation of the Allen-Cahn model by a small term has a large effect on the shape and stability of the interface. In particular, the equilibrium solution now consists of a curved interface. We fully characterize the stability of such an equilibrium in terms of a certain geometric eigenvalue problem, and give a simple geometric interpretation of our stability results.
This is a joint work with David Iron, John Rumsey and Juncheng Wei.
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Theodore Kolokolnikov
2009-01-15
14:00:00 - 15:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
We consider the existence and stability an interface in the singular limit of a perturbed Allen-Cahn model in two dimensions. It is well known that in the unperturbed Allen-Cahn model, the interface boundary evolves according to the mean curvature law which minimizes its perimeter. Therefore the only non-trivial equilibrium state for the unperturbed model consists of a straight interface, typically located at the "neck" of a domain.The perturbation of the Allen-Cahn model by a small term has a large effect on the shape and stability of the interface. In particular, the equilibrium solution now consists of a curved interface. We fully characterize the stability of such an equilibrium in terms of a certain geometric eigenvalue problem, and give a simple geometric interpretation of our stability results.
This is a joint work with David Iron, John Rumsey and Juncheng Wei.