Approximate spectral theory and wave propagation in quasi-periodic media
Benoit, Antoine1; Duerinckx, Mitia2; Gloria, Antoine3; Shirley, Christopher2
1 Université du Littoral Laboratoire de Mathématiques Pures et Appliquées Bâtiment Point Carré 50 Rue Ferdinand Buisson 62100 Calais, France
2 Université Libre de Bruxelles (ULB) Département de mathématiques Campus Plaine CP 213 Boulevard du Triomphe B-1050 Bruxelles, Belgique
3 Sorbonne Université UMR 7598, Laboratoire Jacques-Louis Lions F-75005, Paris, France
Journées équations aux dérivées partielles (2017), Talk no. 5, 12 p.

In this article we make specific in the quasi-periodic setting the general Floquet-Bloch theory we have introduced for stationary ergodic operators together with the associated approximate spectral theory. As an application we consider the long-time behavior of the Schrödinger flow with a quasi-periodic potential (in the regime of small intensity of the discorder), and the long-time behavior of the wave equation with quasi-periodic coefficients (in the homogenization regime).

Published online:
DOI: 10.5802/jedp.655
Benoit, Antoine 1; Duerinckx, Mitia 2; Gloria, Antoine 3; Shirley, Christopher 2

1 Université du Littoral Laboratoire de Mathématiques Pures et Appliquées Bâtiment Point Carré 50 Rue Ferdinand Buisson 62100 Calais, France
2 Université Libre de Bruxelles (ULB) Département de mathématiques Campus Plaine CP 213 Boulevard du Triomphe B-1050 Bruxelles, Belgique
3 Sorbonne Université UMR 7598, Laboratoire Jacques-Louis Lions F-75005, Paris, France 
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Benoit, Antoine; Duerinckx, Mitia; Gloria, Antoine; Shirley, Christopher. Approximate spectral theory  and wave propagation in quasi-periodic media. Journées équations aux dérivées partielles (2017), Talk no. 5, 12 p. doi : 10.5802/jedp.655. http://www.numdam.org/articles/10.5802/jedp.655/

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