Analytic properties of the resolvent for the Helmholtz operator outside a periodic surface

B. Ducomet

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 61, Issue: 3, page 293-314
  • ISSN: 0246-0211

How to cite

top

Ducomet, B.. "Analytic properties of the resolvent for the Helmholtz operator outside a periodic surface." Annales de l'I.H.P. Physique théorique 61.3 (1994): 293-314. <http://eudml.org/doc/76658>.

@article{Ducomet1994,
author = {Ducomet, B.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {periodic Helmholtz operator; decay of the local energy},
language = {eng},
number = {3},
pages = {293-314},
publisher = {Gauthier-Villars},
title = {Analytic properties of the resolvent for the Helmholtz operator outside a periodic surface},
url = {http://eudml.org/doc/76658},
volume = {61},
year = {1994},
}

TY - JOUR
AU - Ducomet, B.
TI - Analytic properties of the resolvent for the Helmholtz operator outside a periodic surface
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 61
IS - 3
SP - 293
EP - 314
LA - eng
KW - periodic Helmholtz operator; decay of the local energy
UR - http://eudml.org/doc/76658
ER -

References

top
  1. [1] C. Gérard, Resonance theory in atom-surface scattering, Commun. Math. Phys., Vol. 126, 1989, pp. 263-290. Zbl0682.47003MR1027498
  2. [2] C. Bardos, J.C. Guillot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non borné: application à la théorie de la diffusion, Comm. in Partial Differential Equations, Vol. 7, 1982, pp. 905-958. Zbl0496.35067MR668585
  3. [3] B. Ducomet, Decay of solutions of the wave equation outside rough surfaces, Preprint PTN-92, 1992. MR1308140
  4. [4] P.D. Lax and R.S. Phillips, Scattering theory, Academic Press, 1989. Zbl0697.35004MR1037774
  5. [5] H.D. Alber, A quasi-periodic boundary value problem for the Laplacian and the continuation of its resolvent, Proc. of the Royal Soc. of Edinburgh, Vol. 82A, 1979, pp. 252-272. Zbl0402.35033MR532908
  6. [6] R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Masson, 1985. Zbl0642.35001
  7. [7] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, T. 1, Dunod, 1968. Zbl0165.10801
  8. [8] J. Giroire, Integral equation methods for exterior problems for the Helmholtz equation, Internal report 40, Centre de Mathématiques Appliquées, École Polytechnique, 1978. 
  9. [9] G.I. Eskin, Boundary value problems for elliptic pseudo-differential equations, AMS Translations, 1981. Zbl0458.35002
  10. [10] M. Reed and B. Simon, Methods of modem mathematical physics, Vol. 4, Academic Press, 1980. Zbl0401.47001MR751959
  11. [11] J. Ralston, Note on the decay of acoustic waves, Duke Math. J., Vol. 46, 1979, pp. 799-804. Zbl0427.35043MR552527
  12. [12] R. Melrose, Singularities and energy decay in acoustical scattering, Duke Math. J.,, Vol. 46, 1979, pp. 43-59. Zbl0415.35050MR523601
  13. [13] B.R. Vainberg, On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as t → ∞ of solutions of non-stationary problems, Russian Math. Surveys, Vol. 30, 1975, pp. 1-58. Zbl0318.35006MR415085

NotesEmbed ?

top

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.