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Finite time extinction for a damped nonlinear Schrödinger equation in the whole space

Bégout, Pascal (2020) Finite time extinction for a damped nonlinear Schrödinger equation in the whole space. Electronic Journal of Differential Equations, 2020 (39). pp. 1-18.

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Abstract

We consider a nonlinear Schrödinger equation set in the whole space with a single power of interaction and an external source. We first establish existence and uniqueness of the solutions and then show, in low space dimension, that the solutions vanish at a finite time. Under a smallness hypothesis of the initial data and some suitable additional assumptions on the external source, we also show that we can choose the upper bound on which time the solutions vanish.

Item Type: Article
Language: English
Date: 28 April 2020
Refereed: Yes
Uncontrolled Keywords: damped Schrödinger equation, existence, uniqueness, finite time extinction, asymptotic behavior
Subjects: G- MATHEMATIQUES
Divisions: Institut de mathématiques de Toulouse
Site: UT1
Date Deposited: 05 May 2020 13:15
Last Modified: 19 May 2020 12:14
URI: http://publications.ut-capitole.fr/id/eprint/34899

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