Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles
type: Item
instance of: scholarly article
title: Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles
zbMATH Open document ID: 0828.35054
author: Morton E. Gurtin
author: H. Mete Soner
author: Panagiotis E. Souganidis
published in: Journal of Differential Equations
publication date: 1995-07-25T00:00:00Z
review text: Consider a region \(\Omega (t)\) in the plane whose boundary curve evolves according to the equation \(B (\Theta) V = G (\Theta) K - U\). Here \(V\) denotes the normal velocity, \(K\) the curvature (measured w.r.t. the outward normal), and \(B (\Theta)\), \(G (\Theta)\) are given functions of the normal-angle \(\Theta\), which is the counterclockwise angle from a fixed axis to the outward normal of \(\partial \Omega (t)\), and \(U\) is a given constant. Assuming that \(B\) and \(G\) are continuous and strictly positive functions, the above equation is of parabolic type with well- behaved solutions. In the present paper the authors relax the assumptions imposed on \(G\): now \(G\) is piecewise continuous, \(\geq 0\) and continuous on any interval of strict positivity. They then show a theorem of existence and local uniqueness and a global comparison theorem for level- set solutions.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35A07
zbMATH DE Number: 768999
zbMATH Keywords: motion of plane region
zbMATH Keywords: viscosity solutions
zbMATH Keywords: global comparison theorem
Wikidata QID: Q57636008
reviewed by: M. Fuchs
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1084
OpenAlex ID: W2057152641
DOI: 10.1006/JDEQ.1995.1084
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description: scientific article; zbMATH DE number 768999