Cet exposé concerne l’approximation faiblement non-linéaire de problèmes aux limites invariants par changement d’échelles.
@article{SLSEDP_2011-2012____A38_0,
author = {Benzoni-Gavage, Sylvie and Coulombel, Jean-Fran\c{c}ois and Tzvetkov, Nikolay},
title = {Ondes de surface faiblement non-lin\'eaires},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:38},
pages = {1--13},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2011-2012},
doi = {10.5802/slsedp.29},
language = {fr},
url = {http://archive.numdam.org/articles/10.5802/slsedp.29/}
}
TY - JOUR AU - Benzoni-Gavage, Sylvie AU - Coulombel, Jean-François AU - Tzvetkov, Nikolay TI - Ondes de surface faiblement non-linéaires JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:38 PY - 2011-2012 SP - 1 EP - 13 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/articles/10.5802/slsedp.29/ DO - 10.5802/slsedp.29 LA - fr ID - SLSEDP_2011-2012____A38_0 ER -
%0 Journal Article %A Benzoni-Gavage, Sylvie %A Coulombel, Jean-François %A Tzvetkov, Nikolay %T Ondes de surface faiblement non-linéaires %J Séminaire Laurent Schwartz — EDP et applications %Z talk:38 %D 2011-2012 %P 1-13 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/articles/10.5802/slsedp.29/ %R 10.5802/slsedp.29 %G fr %F SLSEDP_2011-2012____A38_0
Benzoni-Gavage, Sylvie; Coulombel, Jean-François; Tzvetkov, Nikolay. Ondes de surface faiblement non-linéaires. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 38, 13 p. doi : 10.5802/slsedp.29. http://archive.numdam.org/articles/10.5802/slsedp.29/
[1] G. Alì and J. K. Hunter. Nonlinear surface waves on a tangential discontinuity in magnetohydrodynamics. Quart. Appl. Math., 61(3) :451–474, 2003. | MR | Zbl
[2] S. Benzoni-Gavage. Local well-posedness of nonlocal Burgers equations. Differential Integral Equations, 22(3-4) :303–320, 2009. | MR | Zbl
[3] S. Benzoni-Gavage and M. Rosini. Weakly nonlinear surface waves and subsonic phase boundaries. Comput. Math. Appl., 57(3-4) :1463–1484, 2009. | MR | Zbl
[4] S. Benzoni-Gavage, D. Serre. Multidimensional hyperbolic partial differential equations. Oxford Mathematical Monographs. Oxford University Press, 2007. | MR | Zbl
[5] Sylvie Benzoni-Gavage and Jean-François Coulombel. On the amplitude equations for weakly nonlinear surface waves. Archive for Rational Mechanics and Analysis, 2012. | MR
[6] Sylvie Benzoni-Gavage, Jean-François Coulombel, and Nikolay Tzvetkov. Ill-posedness of nonlocal Burgers equations. Adv. Math., 227(6) :2220–2240, 2011. | MR | Zbl
[7] A. Castro and D. Córdoba. Global existence, singularities and ill-posedness for a nonlocal flux. Adv. Math., 219(6) :1916–1936, 2008. | MR | Zbl
[8] R. Hersh. Mixed problems in several variables. J. Math. Mech., 12 :317–334, 1963. | MR | Zbl
[9] J. K. Hunter. Nonlinear surface waves. In Current progress in hyberbolic systems : Riemann problems and computations (Brunswick, ME, 1988), volume 100 of Contemp. Math., pages 185–202. Amer. Math. Soc., 1989. | MR | Zbl
[10] J. K. Hunter. Short-time existence for scale-invariant Hamiltonian waves. J. Hyperbolic Differ. Equ., 3(2) :247–267, 2006. | MR | Zbl
[11] R. W. Lardner. Nonlinear surface waves on an elastic solid. Internat. J. Engrg. Sci., 21(11) :1331–1342, 1983. | MR | Zbl
[12] A. Marcou. Rigorous weakly nonlinear geometric optics for surface waves. Asymptotic Anal., 69(3-4) :125–174, 2010. | MR | Zbl
[13] D. F. Parker. Waveform evolution for nonlinear surface acoustic waves. Int. J. Engng Sci., 26(1) :59–75, 1988. | Zbl
[14] D. F. Parker and J. K. Hunter. Scale invariant elastic surface waves. In Proceedings of the IX International Conference on Waves and Stability in Continuous Media (Bari, 1997), number 57, pages 381–392, 1998. | MR | Zbl
[15] D. F. Parker and F. M. Talbot. Analysis and computation for nonlinear elastic surface waves of permanent form. J. Elasticity, 15(4) :389–426, 1985. | MR | Zbl
[16] M. V. Safonov. The abstract Cauchy-Kovalevskaya theorem in a weighted Banach space. Comm. Pure Appl. Math., 48(6) :629–637, 1995. | MR | Zbl
[17] D. Serre. Second order initial boundary-value problems of variational type. J. Funct. Anal., 236(2) :409–446, 2006. | MR
Cité par Sources :
