The nonlinear Schrödinger equation on the hyperbolic space
| dc.creator | Banica, Valeria | |
| dc.date | 2004-06-03 | |
| dc.date | 2007-11-29 | |
| dc.date.accessioned | 2026-07-07T08:45:55Z | |
| dc.date.available | 2026-07-07T08:45:55Z | |
| dc.description | In this article we study some aspects of dispersive and concentration phenomena for the Schrödinger equation posed on hyperbolic space $\mathbb{H}^n$, in order to see if the negative curvature of the manifold gets the dynamics more stable than in the Euclidean case. It is indeed the case for the dispersive properties : we prove that the dispersion inequality is valid, in a stronger form than the one on $\mathbb{R}^n$. However, the geometry does not have enough of an effect to avoid the concentration phenomena and the picture is actually worse than expected. The critical nonlinearity power for blow-up turns out to be the same as in the euclidean case, and we prove that there are more explosive solutions for critical and supercritical nonlinearities. | |
| dc.description | 32 pages, final preprint version | |
| dc.identifier | https://arxiv.org/abs/math/0406058 | |
| dc.identifier | http://arxiv.org/abs/math/0406058 | |
| dc.identifier | Comm. P.D.E. 32 (2007), no. 10, 1643-1677 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143118 | |
| dc.subject | Analysis of PDEs | |
| dc.title | The nonlinear Schrödinger equation on the hyperbolic space | |
| dc.type | text |