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arXiv · 2601.19226

The {\L}ojasiewicz-Simon inequality related to grain boundary motion and its applications

Masashi Mizuno·Ayumi Sakiyama·Keisuke Takasao
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Abstract

In this paper, we study the {\L}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 {\L}ojasiewicz-Simon gradient inequality for the grain boundary energy. Finally, we give applications of the inequality to the energy.

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Masashi Mizuno, Ayumi Sakiyama, Keisuke Takasao. 2026-01-27. The {\L}ojasiewicz-Simon inequality related to grain boundary motion and its applications. https://arxiv.org/abs/2601.19226

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