Decomposition of global solutions of bi-laplacian Nonautonomous Schrödinger equations
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911137358938112 |
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| author | Soffer, Avy Wu, Jiayan Wu, Xiaoxu Zhang, Ting |
| author_facet | Soffer, Avy Wu, Jiayan Wu, Xiaoxu Zhang, Ting |
| contents | We study the bi-Laplacian Schrödinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions to such equations decompose asymptotically into a free wave and a weakly localized component in all space dimensions. Moreover, in dimensions $n \geq 9$, we prove that the weakly localized component is in fact spatially localized. The proof is based on a suitably adapted construction of the Free Channel Wave Operator, building on the method recently developed in~\cite{SW20221}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06856 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decomposition of global solutions of bi-laplacian Nonautonomous Schrödinger equations Soffer, Avy Wu, Jiayan Wu, Xiaoxu Zhang, Ting Analysis of PDEs 35Q55 We study the bi-Laplacian Schrödinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions to such equations decompose asymptotically into a free wave and a weakly localized component in all space dimensions. Moreover, in dimensions $n \geq 9$, we prove that the weakly localized component is in fact spatially localized. The proof is based on a suitably adapted construction of the Free Channel Wave Operator, building on the method recently developed in~\cite{SW20221}. |
| title | Decomposition of global solutions of bi-laplacian Nonautonomous Schrödinger equations |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2308.06856 |