M. [. Antuono and . Brocchini, The Boundary Value Problem for the Nonlinear Shallow Water Equations, Studies in Applied Mathematics, vol.445, issue.1, pp.73-93, 2007.
DOI : 10.1017/S002211208700329X

M. Antuono, M. Brocchiniam88-]-yehuda-agnon, and C. C. Mei, Solving the nonlinear shallow-water equations in physical space, Journal of Fluid Mechanics, vol.119, issue.195 2, pp.207-232201, 1988.
DOI : 10.1017/S002211200700835X

M. Brocchini and D. H. Peregrine, Integral flow properties of the swash zone and averaging, Journal of Fluid Mechanics, vol.129, issue.-1, pp.241-273, 1996.
DOI : 10.1016/0378-3839(89)90032-X

G. F. Carriercg58-]-g, H. P. Carrier, ]. Greenspan, F. Dutykh, and . Dias, Gravity waves on water of variable depth Water waves of finite amplitude on a sloping beach Energy of tsunami waves generated by bottom motion, Proc. R. Soc. A, pp.641-65997, 1958.

D. Dutykh, . Th, D. Katsaounis, . Mitsotakis-]-i, E. Didenkulova et al., Finite volume schemes for dispersive wave propagation and runup, Journal of Computational Physics, vol.230, issue.8, pp.3035-3061, 2008.
DOI : 10.1016/j.jcp.2011.01.003
URL : https://hal.archives-ouvertes.fr/hal-00472431

W. Fritz, A. Kongko, B. Moore, J. Mcadoo, C. Goff et al., Extreme runup from the 17 July 2006 Java tsunami, Geophysical Research Letters, vol.144, issue.3???4, p.12602, 2006.
DOI : 10.1029/2007GL029404

L. Géraldine, C. C. Grataloup, and . Mei, Localization of harmonics generated in nonlinear shallow water waves, Phys. Rev. E, vol.68, issue.2, p.26314, 2002.

K. Kajiura, Local behaviour of tsunamis, Waves on Water of Variable Depth, pp.72-79, 1977.
DOI : 10.1007/3540082530_137

J. B. Keller and H. B. Keller, Water wave run-up on a beach Long wave runup on piecewise linear topographies, Department of the Navy, pp.1-28, 1964.

J. W. Miles, Surface-wave scattering matrix for a shelf, Journal of Fluid Mechanics, vol.54, issue.04, pp.755-76727, 1967.
DOI : 10.1121/1.1916327

]. S. Nss-+-11, I. Neetu, R. Suresh, B. Shankar, R. Nagarajan et al., Trapped waves of the 27 november 1945 makran tsunami: observations and numerical modeling Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles Basic coastal engineering 1 [Syn86] C. Synolakis. The runup of long waves [Syn87] C. Synolakis. The runup of solitary waves, Proc. R. Soc. Lond. A, pp.1-10227, 1986.

C. and E. Cachan, Ireland E-mail address: Themistoklis.Stefanakis@cmla.ens-cachan.fr CMLA, ENS Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex E-mail address: Frederic.Dias@ucd, Belfield, Dublin France and School of Mathematical Sciences, vol.4