Electron. J. Differential Equations, Vol. 2020 (2020), No. 39, pp. 1-18.

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

Pascal Begout

We consider a nonlinear Schrodinger 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.

Submitted February 24, 2020. Published April 28, 2020.
Math Subject Classifications: 35Q55, 35A01, 35A02, 35B40, 35D30, 35D35.
Key Words: Damped Schrodinger equation; existence; uniqueness; finite time extinction; asymptotic behavior.

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Pascal Bégout
Institut de Mathématiques de Toulouse
Université Toulouse I Capitole
1, Esplanade de l'Université
31080 Toulouse Cedex 6, France
email: Pascal.Begout@math.cnrs.fr

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