Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions

Abstract

The convergence of schemes for propagation of fronts in a bounded domain moving with normal velocities is studied. The velocities considered depend on the principal curvatures, the normal direction, the location, as well as some nonlocal properties of the front. Most of the schemes considered are in essence threshold dynamics type approximation schemes, modified for Neumann boundary conditions and nonlocal terms. The existence and uniqueness of appropriately defined viscosity solutions of the level-set equations describing the nonlocal motions is also shown.