Quasi-optimal error estimates for the mean curvature flow with a forcing term. (English) Zbl 0820.49019

Bellettini, G.; Paolini, M.

Differ. Integral Equ. 8, No. 4, 735-752 (1995).

A singular perturbed reaction-diffusion equation with a small parameter \(\varepsilon> 0\) is considered. The authors prove a quasi-optimal estimate of order \(O(\varepsilon^ 2|\log \varepsilon|^ 2)\) for the Hausdorff distance between the flow and the approximate interface. The order of the interface error estimate is a consequence of a comparison principle and the explicit construction of suitable sub- and supersolutions.

Reviewer: C.Popa (Iaşi)

MSC:

49Q05	Minimal surfaces and optimization
35K57	Reaction-diffusion equations
35B25	Singular perturbations in context of PDEs
35A35	Theoretical approximation in context of PDEs

Keywords:

mean curvature flow; reaction-diffusion equation; quasi-optimal estimate; Hausdorff distance; interface error estimate