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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, Senegal |
References:
[1] |
G. Allaire, Homogenization and Two-Scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.
doi: 10.1137/0523084. |
[2] |
P. Alliot, E. Frénod and V. Monbet, Modelling the coastal ocean over a time period of several weeks, Journal of Differential Equations, 248 (2010), 639-659.
doi: 10.1016/j.jde.2009.11.004. |
[3] |
E. Audusse, F. Benkhadloun, J. Sainte-Marie and M. Seaid, Multilayer Saint-Venant equations over movable beds, Discrete and Continuous Dynamical Systems - B, 15 (2011), 917-934.
doi: 10.3934/dcdsb.2011.15.917. |
[4] |
C. Berthon, S. Cordier, O. Delestre and M. H. Le, An analytical solution of shallow water system coupled to Exner equation, Comptes Rendus Mathématique, Elsevier, 350 (2012), 183-186.
doi: 10.1016/j.crma.2012.01.007. |
[5] |
S. Cordier, C. Lucas and J. D. D. Zabsonré, A two time-scale model for tidal bed-load transport, Communications in Mathematical Sciences, 10 (2012), 875-888.
doi: 10.4310/CMS.2012.v10.n3.a8. |
[6] |
I. Faye, E. Frénod and D. Seck, Long term behavior of singularity perturbed parabolic degenerated equation, To appear in journal of non linear analysis and application. |
[7] |
D. Idier, D. Astruc and S. J. M. H. Hulcher, Influence of bed roughness on dune and megaripple generation, Geophysical Research Letters, 31 (2004), 1-5.
doi: 10.1029/2004GL019969. |
[8] |
T. Kato, The Cauchy problem for quasi-linear symmetric system, Arch. Ration. Mech. Anal., 58 (1975), 181-205.
doi: 10.1007/BF00280740. |
[9] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Commun. Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[10] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, AMS Translation of Mathematical Monographs, 1968. |
[11] |
J. L. Lions, Remarques sur les équations différentielles ordinaires, Osaka Math. J., 15 (1963), 131-142. |
[12] |
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.
doi: 10.1137/0520043. |
[13] |
L. C. Van Rijn, Handbook on Sediment Transport by Current and Waves, Tech. Report H461:12.1-12.27, Delft Hydraulics, 1989. |
[14] |
J. de D. Zabsonré, C. Lucas and E. Fernandez-Nieto, An energetically consistent viscous sedimentation model, Math. Model. Meth. Appl. Sci., 19 (2009), 477-499.
doi: 10.1142/S0218202509003504. |
show all references
References:
[1] |
G. Allaire, Homogenization and Two-Scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.
doi: 10.1137/0523084. |
[2] |
P. Alliot, E. Frénod and V. Monbet, Modelling the coastal ocean over a time period of several weeks, Journal of Differential Equations, 248 (2010), 639-659.
doi: 10.1016/j.jde.2009.11.004. |
[3] |
E. Audusse, F. Benkhadloun, J. Sainte-Marie and M. Seaid, Multilayer Saint-Venant equations over movable beds, Discrete and Continuous Dynamical Systems - B, 15 (2011), 917-934.
doi: 10.3934/dcdsb.2011.15.917. |
[4] |
C. Berthon, S. Cordier, O. Delestre and M. H. Le, An analytical solution of shallow water system coupled to Exner equation, Comptes Rendus Mathématique, Elsevier, 350 (2012), 183-186.
doi: 10.1016/j.crma.2012.01.007. |
[5] |
S. Cordier, C. Lucas and J. D. D. Zabsonré, A two time-scale model for tidal bed-load transport, Communications in Mathematical Sciences, 10 (2012), 875-888.
doi: 10.4310/CMS.2012.v10.n3.a8. |
[6] |
I. Faye, E. Frénod and D. Seck, Long term behavior of singularity perturbed parabolic degenerated equation, To appear in journal of non linear analysis and application. |
[7] |
D. Idier, D. Astruc and S. J. M. H. Hulcher, Influence of bed roughness on dune and megaripple generation, Geophysical Research Letters, 31 (2004), 1-5.
doi: 10.1029/2004GL019969. |
[8] |
T. Kato, The Cauchy problem for quasi-linear symmetric system, Arch. Ration. Mech. Anal., 58 (1975), 181-205.
doi: 10.1007/BF00280740. |
[9] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Commun. Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[10] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, AMS Translation of Mathematical Monographs, 1968. |
[11] |
J. L. Lions, Remarques sur les équations différentielles ordinaires, Osaka Math. J., 15 (1963), 131-142. |
[12] |
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.
doi: 10.1137/0520043. |
[13] |
L. C. Van Rijn, Handbook on Sediment Transport by Current and Waves, Tech. Report H461:12.1-12.27, Delft Hydraulics, 1989. |
[14] |
J. de D. Zabsonré, C. Lucas and E. Fernandez-Nieto, An energetically consistent viscous sedimentation model, Math. Model. Meth. Appl. Sci., 19 (2009), 477-499.
doi: 10.1142/S0218202509003504. |
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