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Séminaire Laurent Schwartz — EDP et applications

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Sylvie Benzoni-Gavage; Jean-François Coulombel; Nikolay Tzvetkov
Ondes de surface faiblement non-linéaires
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 38, 13 p., doi: 10.5802/slsedp.29
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Résumé - Abstract

Cet exposé concerne l’approximation faiblement non-linéaire de problèmes aux limites invariants par changement d’échelles.

Bibliography

[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 1999831 |  Zbl 1057.35037
[2] S. Benzoni-Gavage. Local well-posedness of nonlocal Burgers equations. Differential Integral Equations, 22(3-4) :303–320, 2009.  MR 2492823 |  Zbl 1240.35446
[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 2509960 |  Zbl 1186.76658
[4] S. Benzoni-Gavage, D. Serre. Multidimensional hyperbolic partial differential equations. Oxford Mathematical Monographs. Oxford University Press, 2007.  MR 2284507 |  Zbl 1113.35001
[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 2960035 |  Zbl pre06102052
[6] Sylvie Benzoni-Gavage, Jean-François Coulombel, and Nikolay Tzvetkov. Ill-posedness of nonlocal Burgers equations. Adv. Math., 227(6) :2220–2240, 2011.  MR 2807088 |  Zbl 1228.35174
[7] A. Castro and D. Córdoba. Global existence, singularities and ill-posedness for a nonlocal flux. Adv. Math., 219(6) :1916–1936, 2008.  MR 2456270 |  Zbl 1186.35002
[8] R. Hersh. Mixed problems in several variables. J. Math. Mech., 12 :317–334, 1963.  MR 147790 |  Zbl 0149.06602
[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 1033516 |  Zbl 0703.35107
[10] J. K. Hunter. Short-time existence for scale-invariant Hamiltonian waves. J. Hyperbolic Differ. Equ., 3(2) :247–267, 2006.  MR 2229856 |  Zbl 1098.35005
[11] R. W. Lardner. Nonlinear surface waves on an elastic solid. Internat. J. Engrg. Sci., 21(11) :1331–1342, 1983.  MR 718407 |  Zbl 0529.73022
[12] A. Marcou. Rigorous weakly nonlinear geometric optics for surface waves. Asymptotic Anal., 69(3-4) :125–174, 2010.  MR 2760337 |  Zbl 1222.35118
[13] D. F. Parker. Waveform evolution for nonlinear surface acoustic waves. Int. J. Engng Sci., 26(1) :59–75, 1988.  Zbl 0627.73022
[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 1708535 |  Zbl 0945.74036
[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 817377 |  Zbl 0587.73032
[16] M. V. Safonov. The abstract Cauchy-Kovalevskaya theorem in a weighted Banach space. Comm. Pure Appl. Math., 48(6) :629–637, 1995.  MR 1338472 |  Zbl 0836.35004
[17] D. Serre. Second order initial boundary-value problems of variational type. J. Funct. Anal., 236(2) :409–446, 2006.  MR 2240169 |  Zbl pre05044059
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