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Article
Relaxation schemes for curvature-dependent front propagation
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
  • S Jin
  • MA Katsoulakis, University of Massachusetts - Amherst
  • ZP Xin
Publication Date
1999
Abstract
In this paper we study analytically and numerically a novel relaxation approximation for front evolution according to a curvature-dependent local law. In the Chapman-Enskog expansion, this relaxation approximation leads to the level-set equation for transport-dominated front propagation, which includes the mean curvature as the next-order term. This approach yields a new and possibly attractive way of calculating numerically the propagation of curvature-dependent fronts. Since the relaxation system is a symmetrizable, semilinear, and linearly convective hyperbolic system without singularities, the relaxation scheme captures the curvature-dependent front propagation without discretizing directly the complicated yet singular mean curvature term.
Pages
1587-1615
Citation Information
S Jin, MA Katsoulakis and ZP Xin. "Relaxation schemes for curvature-dependent front propagation" COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Vol. 52 Iss. 12 (1999)
Available at: http://works.bepress.com/markos_katsoulakis/46/