Semiclassical analysis of dispersion phenomena
Analysis of PDEs
2018-03-26 v1 Mathematical Physics
math.MP
Abstract
Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr{\"o}dinger-type equation in R d. We describe quantitatively the localisation of the energy in a long-time semiclassical limit within this non compact geometry and exhibit conditions under which the energy remains localized on compact sets. We also explain how our results can be applied in a straightforward way to describe obstructions to the validity of smoothing type estimates.
Cite
@article{arxiv.1803.08771,
title = {Semiclassical analysis of dispersion phenomena},
author = {Victor Chabu and Clotilde Fermanian-Kammerer and Fabricio Macià},
journal= {arXiv preprint arXiv:1803.08771},
year = {2018}
}