, Non-dissipative discontinuities in continuum mechanics, 2004.
An introduction to fluid dynamics, 2000. ,
Effective equations for wave propagation in bubbly liquids, J. Fluid Mechanics, vol.153, pp.259-273, 1985. ,
Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics, Commun. Nonlinear Sci. Numer. Simulat, vol.45, pp.245-257, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01232370
Resonant radiation shed by dispersive shock waves, Phys. Rev. A, vol.89, p.13807, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-02393941
, Supersonic flow and shock waves, vol.21, 1999.
, Hyperbolic conservation laws in continuum physics, vol.325, 2000.
On the fully-nonlinear shallow-water generalized Serre equations, Phys. Lett. A, vol.374, pp.1049-1053, 2010. ,
Measure-valued solutions to conservation laws, Archive for Rational Mechanics and Analysis, vol.88, pp.223-270, 1985. ,
Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows, J. Comput. Phys, vol.355, pp.285-309, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01566446
Decay of an initial discontinuity in the defocusing NLS hydrodynamics, Physica D: Nonlinear Phenomena, vol.87, pp.186-192, 1995. ,
Unsteady undular bores in fully nonlinear shallow-water theory, Phys. Fluids, vol.18, p.27104, 2006. ,
Radiating dispersive shock waves in non-local optical media, Proc. R. Soc. A, vol.472, 2016. ,
Dispersive shock waves and modulation theory, Physica D, pp.333-344, 2016. ,
Expansion shock waves in regularized shallow water theory, Proc. Royal Soc. A, vol.472, 2016. ,
Stationary expansion shocks for a regularized Boussinesq system, Studies Appl. Math, vol.140, pp.27-47, 2017. ,
A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves, Nonlinearity, vol.30, issue.7, pp.2718-2736, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01358630
Large amplitude oscillations and their 'thermodynamics' for continua with 'memory, European Journal of Mechanics B/ Fluids, vol.13, issue.6, pp.753-764, 1994. ,
A model of a plug-chain system near the thermodynamic critical point: connection with the Korteweg theory of capillarity and modulation equations, book : IUTAM Symposium on Waves in Liquid/Gas and Liquid/Vapor Two-Phase Systems, pp.419-428, 1995. ,
Generalized vorticity for bubbly liquid and dispersive shallow water equations, Continuum Mechanics and Thermodynamics, vol.13, pp.365-382, 2001. ,
, Bubble effect on Kelvin -Helmholtz instability, vol.16, pp.31-42, 2004.
, , 1991.
On the theory of water waves, Proc. R. Soc. Lond. A, vol.338, pp.43-55, 1974. ,
A derivation of equations for wave propagation in water of variable depth, J. Fluid Mech, vol.78, pp.237-246, 1976. ,
Numerical Approximation of Hyperbolic Systems of Conservation Laws, Applied Mathematical Science, vol.118, 1996. ,
, Nonstationary structure of a collisionless shock wave, vol.38, pp.291-297, 1974.
Dissipationless shock waves in media with positive dispersion, Zh. Eksp. Teor. Fiz, vol.92, pp.1684-1699, 1987. ,
Strong stability preserving high-order time discretization methods, SIAM Review, vol.43, pp.89-112, 2001. ,
On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review, vol.25, pp.35-61, 1983. ,
, Dispersive shock waves, vol.4, p.5562, 2009.
Modulation theory solution for nonlinearly resonant, fifth-order Korteweg -de Vries, nonclassical, travelling dispersive shock waves, Stud. Appl. Math, vol.142, pp.219-240, 2019. ,
Dispersive approximations in fluid mechanics, Communications on Pure and Applied Mathematics, vol.44, issue.1, pp.1-40, 1991. ,
Nonlinear Periodic Waves and Their Modulations: An Introductory Course, 2000. ,
WENOCLAW: A higher order wave propagation method, Hyperbolic Problems: Theory, Numerics, Applications, pp.609-616, 2008. ,
High-order wave propagation algorithm for hyperbolic systems, SIAM J. Sci. Comput, vol.35, issue.1, pp.351-377, 2013. ,
, The Water Waves Problem. Mathematical Surveys and Monographs, vol.188, 2013.
, Amer. Math. Soc
The zero dispersion limit for the KdV equation, I-III, Comm. Pure Appl. Math, vol.36, pp.253-290, 1983. ,
The zero dispersion limit, a deterministic analogue of turbulence, Communications on Pure and Applied Math, vol.44, pp.89-1047, 1991. ,
A numerical scheme for the Green-Naghdi model, J. Comp. Phys, vol.229, pp.2034-2045, 2010. ,
, , 2002.
, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, 2007.
High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model, J. Comp. Physics, vol.257, pp.169-192, 2014. ,
A second long-wave approximation in the Cauchy-Poisson problem Dynamics Cont, Media, vol.77, pp.56-72, 1986. ,
, Material inhomogeneities in elasticity, vol.3, 1993.
Weakly dispersive nonlinear gravity waves, J. Fluid Mechanics, vol.157, pp.519-531, 1985. ,
A one dimensional theory of compressive waves in elastic rod, Proc. 1st US Nat, pp.187-197, 1952. ,
Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, vol.1, issue.4, pp.417-438, 1965. ,
, Behaviour of the Serre equations in the presence of steep gradients revisited, 2017.
The theory of sound, 1945. ,
Well-posedness on large time for a modified full dispersion system of surface waves, J. Math. Phys, vol.53, p.115606, 2012. ,
Contributionà l'étude desécoulements permanents et variables dans les canaux, vol.8, pp.374-388, 1953. ,
Systèmes de lois de conservation (I), Editeur Arts Sciences, 1996. ,
High order weighted essentially nonoscillatory schemes for convection dominated problems, SIAM Review, vol.5, pp.82-126, 2009. ,
An Eulerian interface sharpening algorithm for compressible two-phase flow: The algebraic THINC approach, J. Comput. Phys, vol.268, pp.326-354, 2014. ,
, Shock waves and reactiondiffusion equations 258 Springer Science & Business Media, 2012.
Shock waves in dispersive hydrodynamics with nonconvex dispersion, SIAM J. Appl. Math, vol.77, pp.26-50, 2017. ,
Discontinuous shock solutions of the Whitham modulation equations as dispersionless limits of travelling waves, Nonlinearity, vol.33, pp.3268-3302, 2020. ,
Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements, 2007. ,
Korteweg -de Vries Equation and Generalisations. III. Derivation of the Korteweg -de Vries Equation and Burgers Equation, J. Math. Physics, pp.10-536, 1969. ,
, Hyperbolicity of the modulation equations for the Serre-Green-Naghdi model, 2019.
, Riemann Solvers and Numerical Methods for Fluid Dynamics, 1997.
Equilibrium phase boundaries, Sov. Phys. Dokl, vol.27, pp.551-553, 1982. ,
Kinks versus shocks, In : Shock induced transitions and phase structures in general media, pp.185-229, 1993. ,
Ericksen's bar revisited : energy wiggles, J. Mech. Phys. Solids, vol.44, pp.1371-1408, 1996. ,
The thermodynamic theory of capillarity under the hypothesis of a continuous density variation, J. Stat. Phys, vol.20, pp.200-244, 1893. ,
Linear and Nonlinear Waves, 1974. ,