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Article Dans Une Revue International Mathematics Research Notices Année : 2015

On nonlinear Schrodinger type equations with nonlinear damping

Résumé

We consider equations of nonlinear Schrodinger type augmented by nonlinear damping terms. We show that nonlinear damping prevents finite time blow-up in several situations, which we describe. We also prove that the presence of a quadratic confinement in all spatial directions drives the solution of our model to zero for large time. In the case without external potential we prove that the solution may not go to zero for large time due to (non-trivial) scattering.
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Dates et versions

hal-00799407 , version 1 (12-03-2013)
hal-00799407 , version 2 (01-07-2013)

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Paolo Antonelli, Rémi Carles, Christof Sparber. On nonlinear Schrodinger type equations with nonlinear damping. International Mathematics Research Notices, 2015, 2015, pp.740-762. ⟨10.1093/imrn/rnt217⟩. ⟨hal-00799407v2⟩
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