Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A simple proof of convergence for an approximation scheme for computing motions by mean curvature
SIAM Journal on Numerical Analysis
Asymptotic behavior of solutions of an Allen-Cahn equation with a nonlocal term
Nonlinear Analysis: Theory, Methods & Applications
Convolution-generated motion and generalized Huygens' principles for interface motion
SIAM Journal on Applied Mathematics
A variational method for multiphase volume-preserving interface motions
Journal of Computational and Applied Mathematics
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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.