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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2021

Asymptotic behavior for a dissipative nonlinear Schr\"odinger equation

Résumé

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.

Dates et versions

hal-02908462 , version 1 (29-07-2020)

Identifiants

Citer

Thierry Cazenave, Zheng Han, Ivan Naumkin. Asymptotic behavior for a dissipative nonlinear Schr\"odinger equation. Nonlinear Analysis: Theory, Methods and Applications, 2021, 205, pp.112243. ⟨10.1016/j.na.2020.112243⟩. ⟨hal-02908462⟩
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