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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.06647 |
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| _version_ | 1866908397749665792 |
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| author | Chen, Xinfu Liang, Zhilei |
| author_facet | Chen, Xinfu Liang, Zhilei |
| contents | Allen-Cahn equation is a fundamental continuum model that describes phase transitions in multi-component mixtures. We prove the existence of traveling waves for vector valued Allen-Cahn equations in the context of Ginzburg-Landau theories; in addition, we find the largest wave speed and provide its bounds from upper and below. Our method is based on a variation technique and can be applied to system of equations with a gradient flow structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of traveling waves for vector valued gradient flows Chen, Xinfu Liang, Zhilei Analysis of PDEs 35A15, 35A18, 35C07, 35B40, 35R70 Allen-Cahn equation is a fundamental continuum model that describes phase transitions in multi-component mixtures. We prove the existence of traveling waves for vector valued Allen-Cahn equations in the context of Ginzburg-Landau theories; in addition, we find the largest wave speed and provide its bounds from upper and below. Our method is based on a variation technique and can be applied to system of equations with a gradient flow structure. |
| title | Existence of traveling waves for vector valued gradient flows |
| topic | Analysis of PDEs 35A15, 35A18, 35C07, 35B40, 35R70 |
| url | https://arxiv.org/abs/2506.06647 |