Threshold dynamics type approximation schemes for propagating fronts

Hitoshi Ishii, Gabriel E. Pires, Panagiotis E. Souganidis

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

We study the convergence of general threshold dynamics type approximation schemes to hypersurfaces moving with normal velocity depending on the normal direction and the curvature tensor. We also present results about the asymptotic shape of fronts propagating by threshold dynamics. Our results generalize and extend models introduced in the theories of cellular automaton and motion by mean curvature.

Original languageEnglish
Pages (from-to)267-308
Number of pages42
JournalJournal of the Mathematical Society of Japan
Volume51
Issue number2
Publication statusPublished - 1999 Apr
Externally publishedYes

Fingerprint

Approximation Scheme
Motion by Mean Curvature
Curvature Tensor
Cellular Automata
Hypersurface
Generalise
Model

Keywords

  • Approximation schemes
  • Fronts propagation
  • Level set approach
  • Motion of hypersurfaces
  • Threshold dynamics

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Threshold dynamics type approximation schemes for propagating fronts. / Ishii, Hitoshi; Pires, Gabriel E.; Souganidis, Panagiotis E.

In: Journal of the Mathematical Society of Japan, Vol. 51, No. 2, 04.1999, p. 267-308.

Research output: Contribution to journalArticle

Ishii, H, Pires, GE & Souganidis, PE 1999, 'Threshold dynamics type approximation schemes for propagating fronts', Journal of the Mathematical Society of Japan, vol. 51, no. 2, pp. 267-308.
Ishii, Hitoshi ; Pires, Gabriel E. ; Souganidis, Panagiotis E. / Threshold dynamics type approximation schemes for propagating fronts. In: Journal of the Mathematical Society of Japan. 1999 ; Vol. 51, No. 2. pp. 267-308.
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