Coupling the shallow water equation with a long term dynamics of sand dunes

Mouhamadou Aliou M. T.  Baldé; Diaraf Seck

doi:10.3934/dcdss.2016061

Article Contents

2016, Volume 9, Issue 5: 1521-1551. Doi: 10.3934/dcdss.2016061

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Coupling the shallow water equation with a long term dynamics of sand dunes

Mouhamadou Aliou M. T. Baldé^1, and
Diaraf Seck^1,

1.
Université Cheikh Anta Diop de Dakar, BP 16889 Dakar Fann , Ecole Doctorale de Mathématiques et Informatique, Laboratoire de Mathématiques de la Décision et d'Analyse Numérique, (L.M.D.A.N) F.A.S.E.G

Received: January 31, 2015

Revised: March 31, 2016

Published: September 2016

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Abstract

In this paper we couple a long term dynamic equation of dunes of sand(LTDD) in [6] with a shallow water equation(SWE). And we study the evolution of sand dunes over long periods in the marine environment near the coast. We use works due to S. Klainerman & A. Majda [9] to show on the one hand existence and uniqueness results. On the other hand we give estimations of solutions for the dimensionless coupled system SWE-LTDD. And finally the coupled system is homogenized.

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Mathematics Subject Classification: 35L45, 58J45, 35K15, 58J35, 58J37.

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