On The large Time Asymptotics of Klein-Gordon type equations with General Data
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917551392423936 |
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| author | Soffer, Avy Wu, Xiaoxu |
| author_facet | Soffer, Avy Wu, Xiaoxu |
| contents | We study the Klein-Gordon equation with general interaction terms, which may be linear or nonlinear, and space-time dependent. We initiate the study of such equations with large (non-radial) data. We prove that global solutions are asymptotically given by a free wave and a weakly localized part. The proof is based on constructing in a new way the Free Channel Wave Operator, and further tools from the recent works \cite{Liu-Sof1,Liu-Sof2,SW2020,SW2022}. This work generalizes the results of part of \cite{Liu-Sof1,Liu-Sof2} on the Schrödinger equation to arbitrary dimension, and non-radial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11261 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On The large Time Asymptotics of Klein-Gordon type equations with General Data Soffer, Avy Wu, Xiaoxu Analysis of PDEs Mathematical Physics 35Q55 We study the Klein-Gordon equation with general interaction terms, which may be linear or nonlinear, and space-time dependent. We initiate the study of such equations with large (non-radial) data. We prove that global solutions are asymptotically given by a free wave and a weakly localized part. The proof is based on constructing in a new way the Free Channel Wave Operator, and further tools from the recent works \cite{Liu-Sof1,Liu-Sof2,SW2020,SW2022}. This work generalizes the results of part of \cite{Liu-Sof1,Liu-Sof2} on the Schrödinger equation to arbitrary dimension, and non-radial data. |
| title | On The large Time Asymptotics of Klein-Gordon type equations with General Data |
| topic | Analysis of PDEs Mathematical Physics 35Q55 |
| url | https://arxiv.org/abs/2204.11261 |