Front propagation and phase field theory

G. Barles, H. M. Soner, P. E. Souganidis

Research output: Contribution to journalArticle

246 Scopus citations

Abstract

The connection between the weak theories for a class of geometric equations and the asymptotics of appropriately rescaled reaction-diffusion equations is rigorously established. Two different scalings are studied. In the first, the limiting geometric equation is a first-order equation; in the second, it is a generalization of the mean curvature equation. Intrinsic definitions for the geometric equations are obtained, and uniqueness under a geometric condition on the initial surface is proved. In particular, in the case of the mean curvature equation, this condition is satisfied by surfaces that are strictly starshaped, that have positive mean curvature, or that satisfy a condition that interpolates between the positive mean curvature and the starshape conditions.

Original languageEnglish (US)
Pages (from-to)439-469
Number of pages31
JournalSIAM Journal on Control and Optimization
Volume31
Issue number2
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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