Differential and Integral Equations

A stability criterion for stationary curves to the curvature-driven motion with a triple junction

Ryo Ikota and Eiji Yanagida

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Abstract

A linear stability criterion for stationary curves is presented for the curvature-driven motion with a triple junction. First we perform formal asymptotic expansions and derive a linearized system. Second we investigate eigenvalues of the infinitesimal generator of the system. Finally, through numerical experiments, we demonstrate that the linear criterion determines the stability in the sense of Lyapunov.

Article information

Source
Differential Integral Equations, Volume 16, Number 6 (2003), 707-726.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060608

Mathematical Reviews number (MathSciNet)
MR1973276

Zentralblatt MATH identifier
1036.35029

Subjects
Primary: 35B35: Stability
Secondary: 35K55: Nonlinear parabolic equations 82C24: Interface problems; diffusion-limited aggregation

Citation

Ikota, Ryo; Yanagida, Eiji. A stability criterion for stationary curves to the curvature-driven motion with a triple junction. Differential Integral Equations 16 (2003), no. 6, 707--726. https://projecteuclid.org/euclid.die/1356060608


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