On special properties of solutions to Camassa-Holm equation and related models
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910446178533376 |
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| author | Hong, Christian Linares, Felipe Ponce, Gustavo |
| author_facet | Hong, Christian Linares, Felipe Ponce, Gustavo |
| contents | We study unique continuation properties of solutions to the b-family of equations. This includes the Camassa-Holm and the Degasperi-Procesi models. We prove that for both, the initial value problem and the periodic boundary value problem, the unique continuation results found in \cite{LiPo} are optimal. More precisely, the result established there for the constant $c_0=0$ fails for any constant $c_0\neq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On special properties of solutions to Camassa-Holm equation and related models Hong, Christian Linares, Felipe Ponce, Gustavo Analysis of PDEs Primary: 35Q35, 35B65 Secondary: 76B15 We study unique continuation properties of solutions to the b-family of equations. This includes the Camassa-Holm and the Degasperi-Procesi models. We prove that for both, the initial value problem and the periodic boundary value problem, the unique continuation results found in \cite{LiPo} are optimal. More precisely, the result established there for the constant $c_0=0$ fails for any constant $c_0\neq 0$. |
| title | On special properties of solutions to Camassa-Holm equation and related models |
| topic | Analysis of PDEs Primary: 35Q35, 35B65 Secondary: 76B15 |
| url | https://arxiv.org/abs/2405.08258 |