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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2406.03951 |
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| _version_ | 1866909218368389120 |
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| author | Lee, K. Morales, C. A. |
| author_facet | Lee, K. Morales, C. A. |
| contents | We prove that if the Cauchy problem $\dot{u}=Au$ in a Banach space is hyperbolic, then the problem has the L-shadowing property. Conversely, if the space is finite-dimensional and the L-shadowing property is satisfied, then the problem is hyperbolic. This generalizes a previous result by Ombach \cite{o, o1} for linear homeomorphisms. Some short applications are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | L-shadowing lemma for the Cauchy equation Lee, K. Morales, C. A. Analysis of PDEs Dynamical Systems Primary 54G99, Secondary 37B05 We prove that if the Cauchy problem $\dot{u}=Au$ in a Banach space is hyperbolic, then the problem has the L-shadowing property. Conversely, if the space is finite-dimensional and the L-shadowing property is satisfied, then the problem is hyperbolic. This generalizes a previous result by Ombach \cite{o, o1} for linear homeomorphisms. Some short applications are given. |
| title | L-shadowing lemma for the Cauchy equation |
| topic | Analysis of PDEs Dynamical Systems Primary 54G99, Secondary 37B05 |
| url | https://arxiv.org/abs/2406.03951 |