Scattering for the Beam equation

Benoit Pausader[1]

  • [1] Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, 2, avenue Adolphe Chauvin, 95302 CERGY-PONTOISE cedex, France

Journées Équations aux dérivées partielles (2008)

  • page 1-12
  • ISSN: 0752-0360

How to cite


Pausader, Benoit. "Scattering for the Beam equation." Journées Équations aux dérivées partielles (2008): 1-12. <>.

affiliation = {Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, 2, avenue Adolphe Chauvin, 95302 CERGY-PONTOISE cedex, France},
author = {Pausader, Benoit},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
month = {6},
pages = {1-12},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Scattering for the Beam equation},
url = {},
year = {2008},

AU - Pausader, Benoit
TI - Scattering for the Beam equation
JO - Journées Équations aux dérivées partielles
DA - 2008/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 12
LA - eng
UR -
ER -


  1. Bahouri, H., and Gerard, P., High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. of Math., 121, (1999), 131–175. Zbl0919.35089MR1705001
  2. Bretherton, F.P., Resonant interaction between waves: the case of discrete oscillations, J. Fluid Mech., 20, (1964), 457–479. MR173459
  3. Carles, R. and Gallagher, I., Analyticity of the scattering operator for semilinear dispersive equations, Comm. Math. Phys. to appear. Zbl1173.35677MR2472030
  4. Duyckaerts, T., Holmer, J. and Roudenko, S., Scattering for the non-radial 3d cubic nonlinear Schroedinger equation, Math. Res. Lett. to appear. Zbl1171.35472MR2470397
  5. Glassey, R. T., On the asymptotic behavior of nonlinear wave equations. Trans. Amer. Math. Soc. 182 (1973), 187–200. Zbl0269.35009MR330782
  6. Hebey, E., and Pausader, B., An introduction to fourth order nonlinear wave equations, Lecture notes, 2007, 
  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. Zbl1115.35125MR2257393
  8. Levandosky, S. P., Stability and instability of fourth-order solitary waves, J. Dynam. Diff. Equ., 10, (1998), 151–188. Zbl0893.35079MR1607537
  9. —, Decay estimates for fourth order wave equations, J. Diff. Equ., 143, (1998), 360–413. Zbl0901.35058MR1607964
  10. Levandosky, S. P., and Strauss, W. A., Time decay for the nonlinear beam equation, Methods and Applications of Analysis, 7, (2000), 479–488. Zbl1029.35182MR1869299
  11. Lin, J.E., Local time decay for a nonlinear beam equation, Meth. Appl. Anal., 11 n1, (2004), 65–68. Zbl1210.35251MR2128351
  12. Love, A.E.H., A treatise on the mathematical theory of elasticity, Dover, New York, (1944). Zbl0063.03651MR10851
  13. Miao, C., A note on time decay for the nonlinear beam equation. J. Math. Anal. Appl. 314 (2006), no. 2, 764–773. Zbl1087.35065MR2185265
  14. McKenna, P.J., and Walter, W., Nonlinear oscillations in a suspension bridge, Arch. Rational Mech. Anal., 87, (1987), 167–177. Zbl0676.35003MR866720
  15. —, Traveling waves in a suspension bridge, SIAM J. Appl. Math., 50, (1990), 703–715. Zbl0699.73038MR1050908
  16. Pausader, B., Scattering and the Levandosky-Strauss conjecture for fourth order nonlinear wave equations, J. Diff. Equ., 241 (2), (2007), 237–278. Zbl1145.35090MR2358892
  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. Zbl1170.74028
  19. Payne, L.E. and Sattinger, D.H., Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math., 22, 1975, 273–303. Zbl0317.35059MR402291
  20. Tao, T., A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations, Dynamics of P.D.E. 4 (2007), 1-53. Zbl1142.35088MR2304091

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.