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The grain structure in a one phase system involves grain boundaries (surfaces), three-grain junctions (lines) and four-grain junctions (points). A certain Gibbs energy and mobility can be assigned to each object. System evolution, driven by a decrease in the total Gibbs energy, occurs by migration of objects constrained by rather complex contact conditions. A system with cylindrical symmetry is assumed, where three grain boundaries with different mobilities and different specific Gibbs energies are in contact at a triple junction line of given mobility. The equations of evolution of the system are derived by means of the thermodynamic extremal principle. New general contact conditions at the triple junction are derived, including the mobilities of all objects and the energies, contact angles and curvatures of the grain boundaries. Special contact conditions are also provided for the cases where the triple junction mobility is infinite and/or in the case of one of the grain boundaries having zero mobility. The model is demonstrated by several examples. © 2012 Acta Materialia Inc. Published by Elsevier Ltd.