The Łojasiewicz-Simon inequality related to grain boundary motion and its applications
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| Format: | Preprint |
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2026
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| _version_ | 1866914414157889536 |
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| author | Mizuno, Masashi Sakiyama, Ayumi Takasao, Keisuke |
| author_facet | Mizuno, Masashi Sakiyama, Ayumi Takasao, Keisuke |
| contents | In this paper, we study the Łojasiewicz-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 Łojasiewicz-Simon gradient inequality for the grain boundary energy. Finally, we give applications of the inequality to the energy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19226 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Łojasiewicz-Simon inequality related to grain boundary motion and its applications Mizuno, Masashi Sakiyama, Ayumi Takasao, Keisuke Analysis of PDEs In this paper, we study the Łojasiewicz-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 Łojasiewicz-Simon gradient inequality for the grain boundary energy. Finally, we give applications of the inequality to the energy. |
| title | The Łojasiewicz-Simon inequality related to grain boundary motion and its applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.19226 |