Evolution of grain boundaries

Evolution and trend to equilibrium of a (planar) network of grain boundarie s subject to curvature driven growth is established under the assumption th at the system is initially close to some equilibrium configuration. Curvatu re driven growth is the primary mechanism in processing polycrystalline mat erials to achieve desired texture, ductility, toughness, strength, and othe r properties. Imposition of the Herring condition at triple junctions ensur es that this system is dissipative and that the complementing conditions ho ld. We introduce a new way to employ the known Solonnikov-type estimates, w hich are only local in time, to obtain solutions that are global in time wi th controlled norm. These issues were raised as part of the Mesoscale Inter face Mapping Project.