Long term behaviour of singularly perturbed parabolic degenerated equation

Ibrahima Faye (1) , Emmanuel Frenod (2, 3) , Diaraf Seck (1)

1 L.M.D.A.N - Laboratoire de Mathématique de la Décision et d'Analyse Numérique
2 CALVI - Scientific computation and visualization
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

In this paper we consider models for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.

Mots clés: Space-Time periodic solutions; parabolic PDE degenerated PDE; Singular perturbation; Two-Scale convergence; Homogenization; Sediment transport; Coastal ocean waters; Coastal shelf sedimentology

Domaines: Equations aux dérivées partielles [math.AP]; Interfaces continentales, environnement; Milieux et Changements globaux; Modélisation et simulation

Ibrahima Faye, Emmanuel Frenod, Diaraf Seck. Long term behaviour of singularly perturbed parabolic degenerated equation. 2011. ⟨hal-00592761⟩