D. Bresch and B. Desjardins, Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model, Communications in Mathematical Physics, vol.238, issue.1, pp.211-223, 2003.
DOI : 10.1007/s00220-003-0859-8

D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier???Stokes equations for viscous compressible and heat conducting fluids, Journal de Math??matiques Pures et Appliqu??es, vol.87, issue.1, pp.57-90, 2007.
DOI : 10.1016/j.matpur.2006.11.001
URL : https://hal.archives-ouvertes.fr/hal-00385850

D. Bresch and B. Desjardins, On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier???Stokes models, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.4, pp.362-368, 2006.
DOI : 10.1016/j.matpur.2006.06.005
URL : https://hal.archives-ouvertes.fr/hal-00385847

D. Bresch, B. Desjardins, and D. Gérard-varet, On compressible Navier???Stokes equations with density dependent viscosities in bounded domains, Journal de Math??matiques Pures et Appliqu??es, vol.87, issue.2, pp.227-235, 2007.
DOI : 10.1016/j.matpur.2006.10.010
URL : https://hal.archives-ouvertes.fr/hal-00385852

D. Bresch, M. Gisclon, and C. K. Lin, An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.3, pp.39-477, 2005.
DOI : 10.1051/m2an:2005026
URL : https://hal.archives-ouvertes.fr/hal-00385840

M. J. Castro, E. D. Fernández-nieto, A. M. Ferreiro, and J. A. , García-Rodríguez and C. Parés, High order extensions of Roe schemes for two dimensional nonconservative An energetically consistent viscous sedimentation model 23

M. J. Castro, E. D. Fernández-nieto, A. M. Ferreiro, and C. Parés, Two-dimensional sediment transport models in Shallow Water equations. A second-order finite volume approach over unstructured meshes, Preprint, 2007.

H. J. De-vriend, 2DH mathematical modelling of morphological evolutions in shallow water, 2DH Mathematical Modelling of Morphological Evolutions in Shallow Water, pp.1-27, 1987.
DOI : 10.1016/0378-3839(87)90037-8

H. J. De-vriend, Analysis of horizontally two-dimensional morphological evolutions in shallow water, Journal of Geophysical Research, vol.290, issue.6, pp.92-96, 1987.
DOI : 10.1029/JC092iC04p03877

A. M. Ferreiro, Development of post-process technics of hydrodynamics flux, modelization of sediment transport problems and numerical simulation through finite volume technics, 2006.

A. J. Grass, Sediment transport by waves and currents, SERC London Cent, Mar. Technol. Report No, p.29, 1981.

J. Hudson, Numerical technics for morphodynamic modelling PhD Thesis, 2001.

J. Lions, Quelques méthodes de résolution desprobì emes aux limites non linéaires (Dunod, 1969.

P. Lions, Mathematical Topics in Fluid Mechanics, 1996.

A. Mellet and A. Vasseur, On the Barotropic Compressible Navier???Stokes Equations, Communications in Partial Differential Equations, vol.36, issue.3, pp.431-452, 2007.
DOI : 10.3792/pjaa.55.337

E. Meyer-peter and R. Müller, Formula for bed-load transport, in Rep

P. Orenga, Un th???or???me d'existence de solutions d'un probl???me de shallow water, Archive for Rational Mechanics and Analysis, vol.313, issue.2, pp.183-204, 1995.
DOI : 10.1007/BF00375155

C. Parés and M. J. , Castro On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems, pp.2-38, 2004.

C. Savary, Transcritical transient flow over mobile beds, boundary conditions treatment in a two-layer shallow-water model, 2007.

C. W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics, vol.77, issue.2, pp.439-471, 1998.
DOI : 10.1016/0021-9991(88)90177-5

B. Toumbou, D. L. Roux, and A. Sene, An existence theorem for a 2-D coupled sedimentation shallow-water model, Comptes Rendus Mathematique, vol.344, issue.7, pp.443-446, 2007.
DOI : 10.1016/j.crma.2007.01.026