Self-similar solutions of a 2-D multiple-phase curvature flow

This article studies self-similar shrinking, stationary, and expanding solutions of a two-dimensional motion by curvature equation modelling evolution of grain boundaries in polycrystals. Here the interfacial energy densities are assumed to depend only on the grains and the Herring condition is used for triple junctions (the intersections of three grain boundaries). In particular, in the isotropic case, a total of six configurations are classified as the only self-similar shrinking solutions.