Comptes Rendus
Partial Differential Equations
Internal rectification for elastic surface waves
Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1239-1244.

We prove that fast oscillatory elastic surface waves can produce nontrivial internal nonoscillatory displacements.

We consider elastic surface waves of the form, in y>0:

Uε(t,x,y)k=2εkUk(t,x,y,xctε,yε),
with profiles Uk(t,x,y,Y,θ)=U̲k(t,x,y)+Uk(t,x,θ,Y), where Uk is periodic in θ and exponentially decaying to 0 in Y.

We prove that, in general, the corrector U3 is not purely localized near the boundary, that is U̲3 does not vanish. U3 depends on the slow variable y and does not decay to 0 when Y tends to +∞, even if the source terms are exponentially decaying to 0.

On prouve que des ondes de surface élastiques rapidement oscillantes peuvent produire un déplacement interne non oscillant non trivial.

On considère des ondes de surface élastiques de la forme, sur y>0 :

Uε(t,x,y)k=2εkUk(t,x,y,xctε,yε),
avec des profils Uk(t,x,y,Y,θ)=U̲k(t,x,y)+Uk(t,x,θ,Y), où Uk est périodique en θ et exponentiellement décroissant vers 0 en Y.

On prouve que, en général, le correcteur U3 nʼest pas purement localisé près de la frontière, cʼest-à-dire U̲3 nʼest pas nul. U3 dépend de la variable lente y et ne décroît pas vers 0 lorsque Y tend vers +∞, même si les termes source sont exponentiellement décroissants vers 0.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.07.008

Alice Marcou 1

1 Université de Bordeaux, IMB, 33405 Talence cedex, France
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     title = {Internal rectification for elastic surface waves},
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Alice Marcou. Internal rectification for elastic surface waves. Comptes Rendus. Mathématique, Volume 349 (2011) no. 23-24, pp. 1239-1244. doi : 10.1016/j.crma.2011.07.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.008/

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