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Published in:
Francis K. A. Allotey (Saltpond, Ghana 9 August 1932 – Accra, Ghana 2 November 2017) Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Semiclassical Analysis of Dispersion Phenomena

Authors : Victor Chabu, Clotilde Fermanian-Kammerer, Fabricio Macià

Published in: Analysis and Partial Differential Equations: Perspectives from Developing Countries

Publisher: Springer International Publishing

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Abstract

Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schrödinger-type equation in \(\mathbf{R}^d\). 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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previous chapter Potential Theory Results for a Class of PDOs Admitting a Global Fundamental Solution
next chapter Convergence of Fourier-Walsh Double Series in Weighted
Footnotes
1
Think for instance of \(\lambda (\xi ) = \Vert \xi \Vert ^2\), for which (2) corresponds to the standard, non-semiclassical, Schrödinger equation, one of the most studied dispersive equations.
 
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Metadata
Title
Semiclassical Analysis of Dispersion Phenomena
Authors
Victor Chabu
Clotilde Fermanian-Kammerer
Fabricio Macià
Copyright Year
2019
Book
Analysis and Partial Differential Equations: Perspectives from Developing Countries

Print ISBN: 978-3-030-05656-8

Electronic ISBN: 978-3-030-05657-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-05657-5_7

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