Abstract
A singularly perturbed double obstacle problem is examined as a variational tool for the approximation of the geometric motion of fronts. The relaxation parameter is space-time dependent, thereby allowing the control of transition layer thickness and related interface pointwise accuracy. Optimal order interface error estimates are derived for smooth evolutions. The estimates have a local character for small time, namely they depend on the relaxation parameter local magnitude. The proof is based on constructing suitable sub and supersolutions, which incorporate a number of shape corrections to the basic standing wave profile, and using a modified distance function to the front. Numerical simulations illustrate how the variable transition layer thickness can be exploited in dealing with large curvatures and ultimately in resolving singularities.
Lingua originale | English |
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pagine (da-a) | 173-198 |
Numero di pagine | 26 |
Rivista | Asymptotic Analysis |
Volume | 10 |
DOI | |
Stato di pubblicazione | Pubblicato - 1995 |
Keywords
- Allen-Cahn equation
- mean curvature flow