Threshold dynamics type approximation schemes for propagating fronts

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1999 Apr
Externally publishedYes


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

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Threshold dynamics type approximation schemes for propagating fronts'. Together they form a unique fingerprint.

Cite this