Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916386269298688 |
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| author | Liu, Baiyu Yang, Wenlong |
| author_facet | Liu, Baiyu Yang, Wenlong |
| contents | In this paper, we investigate the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. Firstly, we discuss the properties of solutions in the elliptic space. Then, we establish crucial principles, including the asymptotic narrow region principle.Finally, we employ the method of moving planes to demonstrate the asymptotic symmetry of the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry Liu, Baiyu Yang, Wenlong Analysis of PDEs 35R11, 35B07 In this paper, we investigate the asymptotic symmetry and monotonicity of positive solutions to a reaction-diffusion equation in the unit ball, utilizing techniques from elliptic geometry. Firstly, we discuss the properties of solutions in the elliptic space. Then, we establish crucial principles, including the asymptotic narrow region principle.Finally, we employ the method of moving planes to demonstrate the asymptotic symmetry of the solutions. |
| title | Asymptotic symmetry of solutions for reaction-diffusion equations via elliptic geometry |
| topic | Analysis of PDEs 35R11, 35B07 |
| url | https://arxiv.org/abs/2409.05366 |