Ikota, Ryo; Yanagida, Eiji A stability criterion for stationary curves to the curvature-driven motion with a triple junction. (English) Zbl 1036.35029 Differ. Integral Equ. 16, No. 6, 707-726 (2003). As it is well-known, in some nonlinear diffusive phenomena, systems have three or more stable states. In such systems media are occupied by several regions which correspond to the stable states. In the paper under review, the curvature-driven motion with a triple junction is considered. Namely, the authors investigate the case where a two-dimensional medium is separated into three regions by three curves meeting at one point (called a triple junction). Under some conditions these curves are expected to evolve depending on their curvatures with prescribed angles at the triple junction. The authors perform formal asymptotic expansions and derive a linearized system. To the linearized system they suggest a stability criterion for stationary curves. Besides the eigenvalues of the infinitesimal generator of the system are investigated. Finally, through numerical experiments, it is demonstrated that the linear criterion determines the stability in the sense of Lyapunov. Reviewer: Michael I. Gil’ (Beer-Sheva) Cited in 6 Documents MSC: 35B35 Stability in context of PDEs 35K55 Nonlinear parabolic equations 82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics Keywords:diffusive phenomena; formal asymptotic expansions; systems with several stable states PDFBibTeX XMLCite \textit{R. Ikota} and \textit{E. Yanagida}, Differ. Integral Equ. 16, No. 6, 707--726 (2003; Zbl 1036.35029)