Decomposition of global solutions for a class of nonlinear wave equations
| Autor: | Mavrogiannis, Georgios, Soffer, Avy, Wu, Xiaoxu |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the present paper we consider global solutions of a class of non-linear wave equations of the form \begin{equation*} \Box u= N(x,t,u)u, \end{equation*} where the nonlinearity~$ N(x,t,u)u$ is assumed to satisfy appropriate boundedness assumptions. Under these appropriate assumptions we prove that the free channel wave operator exists. Moreover, if the interaction term~$N(x,t,u)u$ is localised, then we prove that the global solution of the full nonlinear equation can be decomposed into a `free' part and a `localised' part. The present work can be seen as an extension of the scattering results of~\cite{SW20221} for the Schr\"odinger equation. Comment: 29 pages. Comments welcome! |
| Databáze: | arXiv |
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