@incollection{JEDP_2008____A7_0,
author = {Pausader, Benoit},
title = {Scattering for the {Beam} equation},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {7},
pages = {1--12},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2008},
doi = {10.5802/jedp.51},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.51/}
}
Pausader, Benoit. Scattering for the Beam equation. Journées équations aux dérivées partielles (2008), article no. 7, 12 p. doi : 10.5802/jedp.51. http://www.numdam.org/articles/10.5802/jedp.51/
[1] Bahouri, H., and Gerard, P., High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. of Math., 121, (1999), 131–175. | MR | Zbl
[2] Bretherton, F.P., Resonant interaction between waves: the case of discrete oscillations, J. Fluid Mech., 20, (1964), 457–479. | MR
[3] Carles, R. and Gallagher, I., Analyticity of the scattering operator for semilinear dispersive equations, Comm. Math. Phys. to appear. | MR | Zbl
[4] Duyckaerts, T., Holmer, J. and Roudenko, S., Scattering for the non-radial 3d cubic nonlinear Schroedinger equation, Math. Res. Lett. to appear. | MR | Zbl
[5] Glassey, R. T., On the asymptotic behavior of nonlinear wave equations. Trans. Amer. Math. Soc. 182 (1973), 187–200. | MR | Zbl
[6] Hebey, E., and Pausader, B., An introduction to fourth order nonlinear wave equations, Lecture notes, 2007, http://www.u-cergy.fr/rech/pages/hebey/.
[7] Kenig, C., and Merle, F., Global well-posedness, scattering, and blow-up for the energy-critical focusing nonlinear Schrödinger equation in the radial case, Invent. Math. 166 No 3 (2006), 645–675. | MR | Zbl
[8] Levandosky, S. P., Stability and instability of fourth-order solitary waves, J. Dynam. Diff. Equ., 10, (1998), 151–188. | MR | Zbl
[9] —, Decay estimates for fourth order wave equations, J. Diff. Equ., 143, (1998), 360–413. | MR | Zbl
[10] Levandosky, S. P., and Strauss, W. A., Time decay for the nonlinear beam equation, Methods and Applications of Analysis, 7, (2000), 479–488. | MR | Zbl
[11] Lin, J.E., Local time decay for a nonlinear beam equation, Meth. Appl. Anal., 11 n1, (2004), 65–68. | MR
[12] Love, A.E.H., A treatise on the mathematical theory of elasticity, Dover, New York, (1944). | MR | Zbl
[13] Miao, C., A note on time decay for the nonlinear beam equation. J. Math. Anal. Appl. 314 (2006), no. 2, 764–773. | MR | Zbl
[14] McKenna, P.J., and Walter, W., Nonlinear oscillations in a suspension bridge, Arch. Rational Mech. Anal., 87, (1987), 167–177. | MR | Zbl
[15] —, Traveling waves in a suspension bridge, SIAM J. Appl. Math., 50, (1990), 703–715. | MR | Zbl
[16] Pausader, B., Scattering and the Levandosky-Strauss conjecture for fourth order nonlinear wave equations, J. Diff. Equ., 241 (2), (2007), 237–278. | MR | Zbl
[17] —, Scattering in small dimensions for the beam equation, preprint.
[18] Pausader, B., and Strauss, W. A., Analyticity of the Scattering Operator for Fourth-order Nonlinear Waves, preprint.
[19] Payne, L.E. and Sattinger, D.H., Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math., 22, 1975, 273–303. | MR | Zbl
[20] Tao, T., A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations, Dynamics of P.D.E. 4 (2007), 1-53. | MR | Zbl
Cité par Sources :
