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The mathematical model of grain boundary motion, including latticemisorientations' effect, is considered. When time-dependent latticemisorientations are state variables of the surface tension of the grainboundary, to ensure the energy dissipation law, one can obtain a curvature flowof networks with time-dependent mobilities. This paper studies the solvabilityand long-time asymptotic behavior of the curvature flow subjected to theHerring condition which ensures that the constituent grain boundary surfacetensions are balanced at the triple junction.

Long time behavior for a curvature flow of networks related to grain bundary motion with the effect of lattice misorientations