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

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.