RAGE theorem for power bounded operators and decay of local energy for moving obstacles

Vesselin M. Petkov; Vladimir S. Georgiev

Annales de l'I.H.P. Physique théorique (1989)

  • Volume: 51, Issue: 2, page 155-185
  • ISSN: 0246-0211

How to cite

top

Petkov, Vesselin M., and Georgiev, Vladimir S.. "RAGE theorem for power bounded operators and decay of local energy for moving obstacles." Annales de l'I.H.P. Physique théorique 51.2 (1989): 155-185. <http://eudml.org/doc/76463>.

@article{Petkov1989,
author = {Petkov, Vesselin M., Georgiev, Vladimir S.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {local energy decay; periodically moving non-trapping obstacle; monodromy; scattering operator},
language = {eng},
number = {2},
pages = {155-185},
publisher = {Gauthier-Villars},
title = {RAGE theorem for power bounded operators and decay of local energy for moving obstacles},
url = {http://eudml.org/doc/76463},
volume = {51},
year = {1989},
}

TY - JOUR
AU - Petkov, Vesselin M.
AU - Georgiev, Vladimir S.
TI - RAGE theorem for power bounded operators and decay of local energy for moving obstacles
JO - Annales de l'I.H.P. Physique théorique
PY - 1989
PB - Gauthier-Villars
VL - 51
IS - 2
SP - 155
EP - 185
LA - eng
KW - local energy decay; periodically moving non-trapping obstacle; monodromy; scattering operator
UR - http://eudml.org/doc/76463
ER -

References

top
  1. [1] A. Bachelot and V. Petkov, Existence des opérateurs d'ondes pour les systèmes hyperboliques avec un potentiel périodique en temps, Ann. Inst. Henri Poincaré (Physique théorique) t. 47, n° 4, 1987, pp. 383-428. Zbl0657.35102MR933684
  2. [2] J. Cooper and W. Strauss, Energy Boundness and Local Energy Decay of Waves Reflecting off a Moving Obstacle, Indiana Univ. Math. J., t. 25, 1976, pp. 671-690. Zbl0348.35059MR415093
  3. [3] J. Cooper and W. Strauss, Representation of the Scattering Operator for Moving Obstacles, Indiana Univ. Math. J., t. 28, 1979, pp. 643-671. Zbl0427.35056MR542950
  4. [4] J. Cooper and W. Strauss, Scattering of Waves by Periodically Moving Bodies, J. Funct. Anal., t, 47, 1982, pp. 180-229. Zbl0494.35073MR664336
  5. [5] J. Cooper and W. Strauss, Abstract Scattering Theory for Time Periodic Systems with Applications to Electromagnetism, Indiana Univ. Math. J., t. 34, 1985, pp. 33-83. Zbl0582.47011MR773393
  6. [6] J. Cooper and W. Strauss, The Initial Boundary Problem for the Maxwell Equations in the Presence of a Moving Body, S.I.A.M. J. Math. Anal., t. 16, No. 6, 1985, pp. 1165-1179. Zbl0593.35069MR807903
  7. [7] N. Dunford and J. Schwartz, Linear Operators, Part III, Spectral Operators, Wiley Interseciences, New York, 1971. Zbl0243.47001MR412888
  8. [8] V. Georgiev and V. Petkov, Théorème de type RAGE pour des opérateurs à puissances bornées, C.R. Acad. Sci. Paris, T. 303, série I, 1986, pp. 605-608. Zbl0603.47001MR867547
  9. [9] V. Georgiev, Uniform Boundness of the Energy for Time Periodic Potentials, Conference on Operator Theory, Timichoara, 1988, (to appear). Zbl0704.35112MR1090126
  10. [10] L. Hörmander, The Analysis of Linear Partial Differential Operators III, Springer-Verlag, Berlin, Heidelberg, 1985. Zbl0601.35001MR781536
  11. [11] P. Lax and R. Phillips, Scattering Theory, Academic Press, 1967. Zbl0186.16301
  12. [12] P. Lax and R. Phillips, Scattering Theory for the Acoustical Equation in an Even Number of Space Dimensions, Indiana Univ, Math. J., t. 22, 1972, pp. 101-134. Zbl0236.35036MR304882
  13. [13] P. Lax and R. Phillips, Scattering Theory for Dissipative Systems, J. Funct. Anal., t. 14, 1973, pp. 172-233. Zbl0295.35069
  14. [14] R. Melrose, Singularities and Energy Decay in Acoustical Scattering, Duke Math. J., T. 46, 1979, pp. 43-59. Zbl0415.35050MR523601
  15. [15] R. Melrose and J. Sjöstrand, Singularities of Boundary Value Problems I, II, Comm. Pure Appl. Math., t. 31, 1978, pp. 593-617; t. 35, 1982, pp. 129-168. Zbl0368.35020MR492794
  16. [16] C. Morawetz, J. Ralston and W. Strauss, Decay of Solutions of the Wave Equation Outside Non-Tapping Obstacles, Comm. Pure Appl. Math., t. 30, 1977, pp. 447-508. Zbl0372.35008MR509770
  17. [17] V. Petkov, Scattering Theory for Mixed Problems in the Exteriour of Moving Obstacles, pp. 141-155 in Hyperbolic Equations, F. COLOMBINI and M. K. V. MURTHY Ed., Pitman Research Notes in Mathematics Series, 158, Longman Scientific & Technical, 1987. Zbl0732.35065
  18. [18] V. Petkov, Les problèmes inverses de diffusion pour les perturbations dépendant du temps, Séminaire Équations aux Dérivées Partielles, Exposé n° XX, École Polytechnique, 1987-1988. Zbl0682.35103MR1018192
  19. [19] V. Petkov, Scattering Theory for Hyperbolic Operators, North-Holland, Amsterdam, 1989. Zbl0687.35067
  20. [20] G. Popov and Tzv. Rangelov, On the Exponential Growth of the Local Energy for Periodically Moving Obstacles, Osana J. Math. (to appear). Zbl0707.35084
  21. [21] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. III, Scattering Theory, Academic Press, New York, 1979. Zbl0405.47007MR529429
  22. [22] B. Simon, Phase Space Analysis of Simple Scattering Systems: Extension of Some Work of Enss, Duke Math. J., t. 46, 1979, pp. 119-168. Zbl0402.35076MR523604
  23. [23] W. Strauss, The Existence of the Scattering Operator for Moving Obstacles, J. Funct. Anal., t. 31, 1979, pp. 255-262. Zbl0457.35049MR525956
  24. [24] B.R. Vainberg, Asymptotic Methods for the Equations of the Mathematical Physics, Moscow University, 1982 (in Russian). Zbl0518.35002MR700559

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.