Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes

V. M. Petkov

Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990)

  • page 1-12

How to cite

top

Petkov, V. M.. "Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-12. <http://eudml.org/doc/111979>.

@article{Petkov1989-1990,
author = {Petkov, V. M.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {diffusion operator; Dirichlet boundary conditions; obstacles},
language = {fre},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes},
url = {http://eudml.org/doc/111979},
year = {1989-1990},
}

TY - JOUR
AU - Petkov, V. M.
TI - Les singularités du noyau de l'opérateur de diffusion pour des obstacles non-convexes
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1989-1990
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - fre
KW - diffusion operator; Dirichlet boundary conditions; obstacles
UR - http://eudml.org/doc/111979
ER -

References

top
  1. [1] K. Andersson and R. Melrose: The propagation of singularities along gliding rays. Invent. Math., 41 (1977), 197-232. Zbl0373.35053MR494322
  2. [2] F. Cardoso, V. Petkov and L. Stojanov: Singularities of the scattering kernel for generic obstacles. Preprint. Zbl0729.35099
  3. [3] M. Golubitsky and V. Guillemin: Stable Mappings and Their Singularities. Springer Verlag, New York, 1973. Zbl0294.58004MR341518
  4. [4] V. Guillemin: Sojourn time and asymptotic properties of the scattering matrix. Publ. Res. Inst. Math. Sci., Supl. 12 (1977), 69-88. Zbl0381.35064MR448453
  5. [5] P. Lax and R. Phillips: Scattering Theory. Academic Press, New York, 1967. Zbl0186.16301MR217440
  6. [6] A. Majda: A representation formula for the scattering operator and the inverse problem for arbitrary bodies. Comm. Pure Appl. Math.30 (1977), 165-194. Zbl0335.35076MR435625
  7. [7] R. Melrose: Singularities and energy decay of acoustical scattering. Duke Math. J., 46 (1979), 43-59. Zbl0415.35050MR523601
  8. [8] R. Melrose and J. Sjöstrand: Singularities on boundary value problems, I, II. Comm. Pure Appl. Math., 31 (1978), 593-617 and 35 (1982), 129-168. Zbl0546.35083MR492794
  9. [9] S. Nakamura: Singularities of the scattering kernel for two convex obstacles. Publ. RIMS Kyoto University, 25 (1989), 223-238. Zbl0699.35202MR1003786
  10. [10] S. Nakamura and H. Soga: Singularities of the scattering kernel for two balls. J. Math. Soc. Japan, 40 (1988), 205-220. Zbl0638.35068MR930597
  11. [11] V. Petkov: High frequency asymptotics of the scattering amplitude for non-convex bodies. Comm. PDE, 5 (1980), 293-329. Zbl0435.35065MR562545
  12. [12] V. Petkov: Scattering Theory for Hyperbolic Operators. North-Holland, Amsterdamn, 1989. Zbl0687.35067MR1028780
  13. [13] V. Petkov and L. Stojanov: Periods of multiple reflecting geodesics and inverse spectral results. Amer. J. Math., 109 (1987), 619-668. Zbl0652.35027MR900034
  14. [14] V. Petkov and L. Stojanov: Spectrum of the Poincaré map for periodic reflecting rays in generic domains, Math. Z., 194 (1987), 505-518. Zbl0673.58035MR881708
  15. [15] V. Petkov and L. Stojanov: On the number of periodic rays in generic domains. Ergodic Theory and Dynamical Systems, 8 (1988), 81-91. Zbl0668.58005MR939062
  16. [16] V. Petkov and L. Stojanov: Singularities of the scattering kernel and scattering invariants for several strictly convex obstacles. Trans. Amer. Math. Soc.312 (1989), 203-235. Zbl0685.35083MR929661
  17. [17] V. Petkov and L. Stojanov: Singularities of the scattering kernel for a class of starshaped non-convex obstacles. Math. Appl. Comput., (to appear). Zbl0705.35095
  18. [18] H. Soga: Conditions against rapid decrease of oscillatory integrals and their applications to inverse scattering problems. OsanaJ. Math., 23 (1986), 441-456. Zbl0617.35104MR856897
  19. [19] L. Stojanov: Unpublished manuscript, 1989. 
  20. [20] L. Stojanov: Nonexistence of generalized scattering rays and singularities of the scattering kernel for generic domains in R3. Preprint, 1989. Zbl0742.58056
  21. [21] B. Vainberg: Asymptotic Methods in Equations of Mathematical Physics. Gordon and Breach Sci. Publ., 1988. Zbl0743.35001MR1054376

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.