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.
Original language | English |
---|---|
Pages (from-to) | 173-198 |
Number of pages | 26 |
Journal | Asymptotic Analysis |
Publication status | Published - 1995 |
Keywords
- Allen-Cahn equation
- mean curvature flow