Instability of stationary solutions for equations of curvature-driven motion of curves
type: Item
instance of: scholarly article
title: Instability of stationary solutions for equations of curvature-driven motion of curves
zbMATH Open document ID: 0834.35019
DOI: 10.1007/BF02219370
author: Shin-Ichiro Ei
author: Eiji Yanagida
published in: Journal of Dynamics and Differential Equations
publication date: 1995-09-25T00:00:00Z
review text: The authors study the equations of evolving curves on a two-dimensional square domain \(\Omega\). Here, the curve is assumed to move depending on its curvature, normal vector, and position, and to intersect \(\partial \Omega\) orthogonally at its endpoints. The solutions are considered in the viscosity sense. In a special case the curvature equation together with the boundary condition strongly resembles an ODE with homogeneous Neumann boundary conditions. Using this connection, the authors prove the instability of stationary solutions through an eigenvalue analysis, provided certain conditions are satisfied.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 800416
zbMATH Keywords: curvature flow of curves
zbMATH Keywords: instability of stationary solutions
zbMATH Keywords: viscosity solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 800416