The ojasiewicz-Simon inequality related to grain boundary motion and its applications
Abstract
In this paper, we study the ojasiewicz-Simon gradient inequality for the mathematical model of grain boundary motion. We first derive a curve shortening equation with time-dependent mobility, which guarantees the energy dissipation law for the grain boundary energy, including the difference between orientations of the constituent grains as a state variable. Next, we discuss the ojasiewicz-Simon gradient inequality for the grain boundary energy. Finally, we give applications of the inequality to the energy.
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