Singularly perturbed degenerated parabolic equations andapplication to seabed morphodynamics in tided environment

Ibrahima Faye; Emmanuel Frénod; Diaraf Seck

doi:10.3934/dcds.2011.29.1001

Article Contents

2011, Volume 29, Issue 3: 1001-1030. Doi: 10.3934/dcds.2011.29.1001

This issue Previous Article Almost periodic solutions for a class of semilinear quantum harmonic oscillators Next Article Linearization of cohomology-free vector fields

Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment

1.
Université de Bambey, BP 30 Bambey, Ecole Doctorale de Mathématiques et Informatique, Laboratoire de Mathématiques de la Décision et d'Analyse Numérique, F.A.S.E.G/F.S.T
2.
Université Européenne de Bretagne, Lab-STICC (UMR CNRS 3192), Université de Bretagne-Sud, Centre Yves Coppens, Campus de Tohannic, F-56017, Vannes
3.
Université Cheikh Anta Diop de Dakar, BP 16 889, Dakar-Fann. E.D. de Mathématiques et Informatique, Laboratoire de Mathématiques de la Décision et d'Analyse Numérique, F.A.S.E.G/F.S.T

Received: December 31, 2009

Revised: June 30, 2010

Published: August 2011

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Abstract

In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.

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Mathematics Subject Classification: Primary: 35K65, 35B25, 35B10 ; Secondary: 92F05, 86A60.

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