Journal of the Mathematical Society of Japan

Threshold dynamics type approximation schemes for propagating fronts

Hitoshi ISHII, Gabriel E. PIRES, and Panagiotis E. SOUGANIDIS

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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.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 2 (1999), 267-308.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108018

Digital Object Identifier
doi:10.2969/jmsj/05120267

Mathematical Reviews number (MathSciNet)
MR1674750

Zentralblatt MATH identifier
0935.53006

Subjects
Primary: 53A99: None of the above, but in this section 45L05: Theoretical approximation of solutions {For numerical analysis, see 65Rxx} 35B40: Asymptotic behavior of solutions

Keywords
Motion of hypersurfaces fronts propagation threshold dynamics level set approach approximation schemes

Citation

ISHII, Hitoshi; E. PIRES, Gabriel; E. SOUGANIDIS, Panagiotis. Threshold dynamics type approximation schemes for propagating fronts. J. Math. Soc. Japan 51 (1999), no. 2, 267--308. doi:10.2969/jmsj/05120267. https://projecteuclid.org/euclid.jmsj/1213108018


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