The {\L}ojasiewicz-Simon inequality related to grain boundary motion and its applications
Analysis of PDEs
2026-03-24 v2
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.
Keywords
Cite
@article{arxiv.2601.19226,
title = {The {\L}ojasiewicz-Simon inequality related to grain boundary motion and its applications},
author = {Masashi Mizuno and Ayumi Sakiyama and Keisuke Takasao},
journal= {arXiv preprint arXiv:2601.19226},
year = {2026}
}
Comments
32 pages, 1 figures