Bégout, Pascal and Diaz, Jesus Ildefonso (2006) On a nonlinear Schrödinger equation with a localizing effect. Comptes rendus. Mathematique, 342 (7). pp. 459-463.

[thumbnail of Begout_35021.pdf]
Preview
Text
Download (240kB) | Preview

Abstract

We consider the nonlinear Schrödinger equation associated to a singular potential of the form
$a|u|^{-(1-m)}u+bu,$ for some $m\in(0,1),$ on a possible unbounded domain. We use some suitable energy methods to prove that if $\mathrm{Re}(a)+\mathrm{Im}(a)>0$ and if the initial and right hand side data have compact support then any possible solution must also have a compact support for any $t>0.$ This property contrasts with the behavior of solutions associated to regular potentials $(m\ge1).$ Related results are proved also for the associated stationary problem and for self-similar solution on the whole space and potential $a|u|^{-(1-m)}u.$ The existence of solutions is obtained by some compactness methods under additional conditions.

Item Type: Article
Language: English, French
Date: 2006
Refereed: No
Subjects: G- MATHEMATIQUES
Divisions: Institut de mathématiques de Toulouse
Site: UT1
Date Deposited: 26 May 2020 14:18
Last Modified: 27 Oct 2021 13:38
URI: https://publications.ut-capitole.fr/id/eprint/35021
View Item

Downloads

Downloads per month over past year