The tendency to equilibrium of a planar network of grain boundaries, subject to curvature-driven growth, was considered. It was assumed that the system was initially close to some equilibrium configuration. Imposition of the Herring condition at triple-junctions ensured that the system was dissipative. A new method was used to incorporate known Solonnikov-type estimates, which were only local in time, so as to obtain solutions which were global in time.

Evolution of Grain Boundaries. D.Kinderlehrer.Kinderlehrer, C.Liu: Mathematical Models and Methods in Applied Sciences, 2001, 11[4], 713-29