Threshold dynamics type approximation schemes for propagating fronts

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

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 journal › Article › peer-review

59 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 language	English
Pages (from-to)	267-308
Number of pages	42
Journal	Journal of the Mathematical Society of Japan
Volume	51
Issue number	2
Publication status	Published - 1999 Apr
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "Threshold dynamics type approximation schemes for propagating fronts",

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.",

keywords = "Approximation schemes, Fronts propagation, Level set approach, Motion of hypersurfaces, Threshold dynamics",

author = "Hitoshi Ishii and Pires, {Gabriel E.} and Souganidis, {Panagiotis E.}",

year = "1999",

month = apr,

language = "English",

volume = "51",

pages = "267--308",

journal = "Journal of the Mathematical Society of Japan",

issn = "0025-5645",

publisher = "Mathematical Society of Japan - Kobe University",

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TY - JOUR

T1 - Threshold dynamics type approximation schemes for propagating fronts

AU - Ishii, Hitoshi

AU - Pires, Gabriel E.

AU - Souganidis, Panagiotis E.

PY - 1999/4

Y1 - 1999/4

N2 - 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.

AB - 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.

KW - Approximation schemes

KW - Fronts propagation

KW - Level set approach

KW - Motion of hypersurfaces

KW - Threshold dynamics

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M3 - Article

AN - SCOPUS:0000115247

SN - 0025-5645

VL - 51

SP - 267

EP - 308

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 2

ER -

Threshold dynamics type approximation schemes for propagating fronts

Abstract

Keywords

ASJC Scopus subject areas

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