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Long-time behaviour for weakly damped driven nonlinear Schrödinger equations in ${ℝ}^{N},N\le 3$. (English) Zbl 0828.35125
Summary: We study the long-time behaviour of solutions to nonlinear Schrödinger equations with a zero order dissipation and an additional external force, when the space variable $x$ varies over ${ℝ}^{N}$, $N\le 3$. We prove that the long-time behaviour is described by a maximal compact attractor for the strong topology of ${H}^{1}\left({ℝ}^{N}\right)$.
##### MSC:
 35Q55 NLS-like (nonlinear Schrödinger) equations 35B40 Asymptotic behavior of solutions of PDE
##### References:
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