Asymptotic behavior for a dissipative nonlinear Schr\'odinger equation
| Autor: | Cazenave, Thierry, Han, Zheng, Naumkin, Ivan |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.na.2020.112243 |
| Popis: | We consider the Schr\"odinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +\Delta u=\lambda|u|^{\alpha}u \end{equation*} in ${\mathbb R}^N $, $N\geq1$, where $\lambda\in {\mathbb C} $ with $\Im\lambda<0$. Assuming $\frac {2} {N+2}<\alpha<\frac2N$, we give a precise description of the long-time behavior of the solutions (including decay rates in $L^2$ and $L^\infty $, and asymptotic profile), for a class of arbitrarily large initial data. |
| Databáze: | arXiv |
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