Équipartition de l'énergie pour les systèmes hyperboliques et formes compatibles

Alain Bachelot

Annales de l'I.H.P. Physique théorique (1987)

  • Volume: 46, Issue: 1, page 45-76
  • ISSN: 0246-0211

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Bachelot, Alain. "Équipartition de l'énergie pour les systèmes hyperboliques et formes compatibles." Annales de l'I.H.P. Physique théorique 46.1 (1987): 45-76. <http://eudml.org/doc/76351>.

@article{Bachelot1987,
author = {Bachelot, Alain},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {finite energy solution; compatible; hermitian systems; equipartition of energy; Klein-Gordon equation; Maxwell's equations; Dirac system; Neutrino equation},
language = {fre},
number = {1},
pages = {45-76},
publisher = {Gauthier-Villars},
title = {Équipartition de l'énergie pour les systèmes hyperboliques et formes compatibles},
url = {http://eudml.org/doc/76351},
volume = {46},
year = {1987},
}

TY - JOUR
AU - Bachelot, Alain
TI - Équipartition de l'énergie pour les systèmes hyperboliques et formes compatibles
JO - Annales de l'I.H.P. Physique théorique
PY - 1987
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 45
EP - 76
LA - fre
KW - finite energy solution; compatible; hermitian systems; equipartition of energy; Klein-Gordon equation; Maxwell's equations; Dirac system; Neutrino equation
UR - http://eudml.org/doc/76351
ER -

References

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  1. [1] G.S.S. Avila et D.G. Costa, Decay of solutions of symmetric hyperbolic systems of partial differential equations, Rocky Mountain J. Math., t. 9, n° 3, 1979, p. 405-413. Zbl0425.35070MR528739
  2. [2] G.S.S. Avila et D.G. Costa, Asymptotic properties of general symmetric hyperbolic systems, J. Funct. Anal., t. 35, 1980, p. 49-63. Zbl0432.35053MR560217
  3. [3] A. Bachelot, Régularité microlocale de produits dans les espaces de type Lp et propagation des singularités. Publications de l'Université de Bordeaux I, n° 8407. 
  4. [4] A. Bachelot, B. Hanouzet, Applications bilinéaires compatibles avec un système différentiel à coefficients variables. C. R. Acad. Sc. Paris, t. 299, série I, n° 12, 1984, p. 543-546. Zbl0561.47040MR770442
  5. [5] A. Bachelot, Équipartition de l'énergie pour les systèmes hyperboliques et formes compatibles, C. R. Acad. Sci. Paris, t. 301, série I, n° 11, 1985, p. 573-576. Zbl0601.35067MR816632
  6. [6] C. Bardos et D.G. Costa, Decay along non-bicharacteristic says of solutions of first order hyperbolic systems, J. Math. Pures Appl., t. 53, 1974, p. 427-435. Zbl0305.35068MR374687
  7. [7] L.E. Bobisud, J. Calvert, Energy bounds and virial theorems for abstract wave equation, Pacific J. Math., t. 47, 1973, p. 27-37. Zbl0263.35053MR326200
  8. [8] A.R. Brodsky, On the asymptotic behavior of solutions of the wave equation, Proc. A. M. S., t. 18, 1967, p. 207-208. Zbl0149.06704MR212417
  9. [9] D.G. Costa, On partition of energy uniformly propagative systems, J. Math. Anal. App., t. 58, 1977, p. 56-62. Zbl0354.35061MR470505
  10. [10] D.G. Costa et W.A. Strauss, Energy splitting, Quart. Appl. Math., t. 39, 1981, p. 351-361. Zbl0478.35062MR636240
  11. [11] G. Dassios, Equipartition of energy in elastic wave propagation, Mech. Res. Comm., t. 6 (1), 1979, p. 45-50. Zbl0416.73022MR524233
  12. [12] G. Dassios, Equipartition of energy for Maxwell's equations, Quart. Appl. Mat., t. 37 (4), 1980, p. 465-469. Zbl0425.35082MR564738
  13. [13] G. Dassios, Energy theorems for magnetoelastic waves in a perfectly conducting medium, Quart. Appl. Math., t. 39 (4), 1982, p. 479-490. Zbl0507.73091MR644102
  14. [14] G. Dassios, Finite time equipartition for second-order hyperbolic systems. I. M. A., J. Appl. Math., t. 29, 1982, p. 197-202. Zbl0508.35050MR679228
  15. [15] G. Dassios, E. Galanis, Asymptotic equipartition of kinetic and strain energy for elastic waves in anisotropic media, Quart. Appl. Math., t. 38 (1), 1980, p. 121-128. Zbl0436.73014MR575835
  16. [16] G. Dassios, M. Grillakis, Equipartition of energy for anisotropic elastic waves, J. Diff. Equat., t. 51, 1984, p. 408-418. Zbl0487.73032MR735206
  17. [17] G. Dassios, M. Grillakis, Dissipation rates and partition of energy in thermo–elasticity, Arch. Rational Mech. Anal., t. 87, 1984, p. 49-91. Zbl0563.73007MR760319
  18. [18] G. Dassios, M. Grillakis, Equipartition of energy in scattering theory, S. I. A. M., J. Math. Anal., t. 14, 1983, p. 915-924. Zbl0525.35068MR711172
  19. [19] G. Dassios, M. Grillakis, Asymptotic equipartition rate for wave motion in an even number of space dimensions, à paraître in J. Math. Anal. Appl. Zbl0619.35067MR861907
  20. [20] R.J. Duffin, Equipartition of energy in wave motion, J. Math. Anal. Appl., t. 32, 1970, p. 386-391. Zbl0223.35055MR269190
  21. [21] R.T. Glassey, On the asymptotic behavior of nonlinear wave equations, Trans. A. M. S., t. 182, 1973, p. 187-200. Zbl0269.35009MR330782
  22. [22] R.T. Glassey, W.A. Strauss, Propagation of the energy of Yang-Mills fields, in: Bifurcation phenomena in mathematical physics (ed. D. Bessis et C. Bardos), Reidel Publ. Co, p. 231-241. 
  23. [23] J.A. Goldstein, An asymptotic property of solutions of wave equations, Proc. Amer. Math. Soc., t. 23, 1969, p. 359-363. Zbl0185.34103MR250125
  24. [24] J.A. Goldstein, An asymptotic property of solutions of wave equations II, J. Math. Anal. Appl., t. 32, 1970, p. 392-399. Zbl0216.41803MR267281
  25. [25] J.A. Goldstein, S.J. Rosencrans, Energy decay and partition for dissipative wave equations, J. Diff. Equat., t. 36, 1980, p. 66-73. Zbl0403.35096MR571128
  26. [26] J.A. Goldstein, J.T. Sandefur (Jr), Asymptotic equipartition of energy for differential equations in Hilbert Space, Trans. Amer. Math. Soc., t. 219, 1976, p. 397-406. Zbl0302.34080MR410016
  27. [27] J.A. Goldstein, J. T. Sandefur ( Jr), Abstract equipartition of energy theorems, J. Math. Appl., t. 67, 1979, p. 58-74. Zbl0403.47011MR524462
  28. [28] K. Hamdache, Existence globale et comportement asymptotique pour des systèmes hyperboliques semi-linéaires, C. R. Acad. Sci. Paris, t. 297, 1983, p. 619-622. Zbl0554.35076MR735128
  29. [29] B. Hanouzet, Applications bilinéaires compatibles avec un système à coefficients variables. Continuité dans les espaces de Besov, C. P. D. E., t. 10 (4), 1985, p. 433-465. Zbl0572.35032MR784684
  30. [30] B. Hanouzet, J.L. Joly, Applications bilinéaires sur certains sous-espaces de type Sobolev, C. R. Acad. Sci. Paris, t. 294, 1982, p. 745-747. Zbl0524.46017MR668575
  31. [31] B. Hanouzet, J.L. Joly, Formes multilinéaires sur des sous-espaces de distributions, Publication de l'Université de Bordeaux I, n° 8203. Zbl0491.35087
  32. [32] B. Hanouzet, J.L. Joly, Bilinear maps compatible with a system, in: Contributionsto nonlinear partial differential equations (C. Bardos, A. Damlamian, I. J. Diaz, J. Hernandez, eds), Research Notes in Math., t. 89, Pitman Advanced Publishing Program, 1983. Zbl0542.35005
  33. [33] B. Hanouzet, J.L. Joly, Applications bilinéaires compatibles avec un système hyperbolique, C. R. Acad. Sci. Paris, t. 301, série I, 1985, p. 491-494. Zbl0601.35066MR812565
  34. [34] H.A. Levine, An equipartition of energy theorem for weak solutions of evolutionary equations in Hilbert space: the Lagrange identity method. J. Diff. Equat., t. 24, 1977, p. 197-210. Zbl0398.34056MR437874
  35. [35] K. Mochizuki, Asymptotic property of solutions of some higher order hyperbolic equations I, Proc. Japan Acad., t. 46, 1970, p. 262-272. Zbl0245.35052MR283436
  36. [36] R.S. Strichartz, Asymptotic behavior of waves, J. Funct. Anal., t. 40, 1981, p. 341- 357. Zbl0484.35070MR611588
  37. [37] C.H. Wilcox, Asymptotic wave functions and energy distributions in strongly propagative anisotropic media, J. Math. Pures Appl., t. 57, 1978, p. 275-321. Zbl0409.35064MR513101

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