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
Pascal Begout
Abstract:
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.
DOI: 10.58997/ejde.2020.39
Show me the PDF file (381 KB), TEX file for this article.
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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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