Semiclassical analysis of dispersion phenomena
Abstract
Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr\"odinger-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.
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