Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times

S. R. Czapor; R. G. McLenaghan; F. D. Sasse

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 71, Issue: 6, page 595-620
  • ISSN: 0246-0211

How to cite

top

Czapor, S. R., McLenaghan, R. G., and Sasse, F. D.. "Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times." Annales de l'I.H.P. Physique théorique 71.6 (1999): 595-620. <http://eudml.org/doc/76846>.

@article{Czapor1999,
author = {Czapor, S. R., McLenaghan, R. G., Sasse, F. D.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Huygens' principle; conformally invariant scalar wave equation; non-selfadjoint scalar wave equation},
language = {eng},
number = {6},
pages = {595-620},
publisher = {Gauthier-Villars},
title = {Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times},
url = {http://eudml.org/doc/76846},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Czapor, S. R.
AU - McLenaghan, R. G.
AU - Sasse, F. D.
TI - Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 6
SP - 595
EP - 620
LA - eng
KW - Huygens' principle; conformally invariant scalar wave equation; non-selfadjoint scalar wave equation
UR - http://eudml.org/doc/76846
ER -

References

top
  1. [1] W.G. Anderson, R.G. McLenaghan and F.D. Sasse, Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times, Ann. Inst. Henri Poincaré, Phys. Théor.70 (1999) 259-276. Zbl0956.83005MR1718182
  2. [2] L. Asgeirsson, Some hints on Huygens' principle and Hadamard's conjecture, Comm. Pure Appl. Math.9 (1956) 307-326. Zbl0074.31101MR82034
  3. [3] J. Carminati and R.G. McLenaghan, Determination of all Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle, Phys. Lett.105A (1984) 351-354. MR766032
  4. [4] J. Carminati and R.G. McLenaghan, Some new results on the validity of Huygens' principle for the scalar wave equation on a curved space-time, in: Proceedings of the Journées Relativistes 1984, Aussois, France, edited by Laboratoire Gravitation et Cosmologie Relativistes, Institut Henri Poincaré, Lecture Notes in Physics, vol. 212, Springer, Berlin, 1984. Zbl0557.53046MR780225
  5. [5] J. Carminati and R.G. McLenaghan, An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor.44 (1986) 115-153. Zbl0595.35067MR839281
  6. [6] J. Carminati and R.G. McLenaghan, An explicit determination of spacetimes on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part II: Petrov type D space-times, Ann. Inst. Henri Poincaré, Phys. Théor.47 (1987) 337-354. Zbl0694.35074MR933681
  7. [7] J. Carminati and R.G. McLenaghan, An explicit determination of space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III: Petrov type III space-times, Ann. Inst. Henri Poincaré, Phys. Théor.48 (1988) 77-96. Zbl0706.35131MR947160
  8. [8] J. Carminati, S.R. Czapor, R.G. McLenaghan and G.C. Williams, Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times, Ann. Inst. Henri Poincaré, Phys. Théor.54 (1991) 9-16. Zbl0729.35075MR1102968
  9. [9] S.R. Czapor, Solving algebraic equations: Combining Buchberger's algorithm with multivariate factorization, J. Symbolic Comput.7 (1989) 49-53. Zbl0668.68033MR984270
  10. [10] S.R. Czapor and R.G. McLenaghan, NP: A Maple package for performing calculations in the Newman-Penrose formalism, Gen. Rel. Gravit.19 (1987) 623- 635. Zbl0613.53033MR892637
  11. [11] S.R. Czapor, R.G. McLenaghan and J. Carminati, The automatic conversion of spinor equations to dyad form in MAPLE, Gen. Rel. Gravit.24 (1992) 911-928. Zbl0758.53047MR1180241
  12. [12] J.-C. Faugère, Résolution des systemes d'équation algébriques, Ph.D. Thesis, Université Paris, 1994. 
  13. [13] K.O. Geddes, S.R. Czapor and G. Labahn, Algorithms for Computer Algebra, Kluwer, Norwell, MA, 1992. Zbl0805.68072MR1256483
  14. [14] P. Günther, Zur Gültigkeit des huygensschen Prinzips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus, S.-B. Sachs. Akad. Wiss. Leipzig Math.-Natur. K.100 (1952) 1-43. Zbl0046.32201MR50136
  15. [15] J. Hadamard, Lectures on Cauchy's Problem in Linear Differential Equations, Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
  16. [16] J. Hadamard, The problem of diffusion of waves, Ann. of Math.35 (1942) 510- 522. Zbl0063.01841MR6809
  17. [17] M. Mathisson, Le probléme de M. Hadamard relatif à la diffusion des ondes, Acta Math.71 (1939) 249-282. Zbl0022.22802MR728
  18. [18] R.G. McLenaghan, An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle, Proc. Cambridge Philos. Soc. (1969). Zbl0182.13403MR234700
  19. [19] R.G. McLenaghan and F.D. Sasse, Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor.65 (1996) 253-271. Zbl0869.53061MR1420704
  20. [20] R.G. McLENAGHAN and T.F. Walton, An explicit determination of the non-selfadjoint wave equations on a curved space-time that satisfies Huygens' principle. Part I: Petrov type N background space-times, Ann. Inst. Henri Poincaré, Phys. Théor.48 (1988) 267-280. Zbl0645.53047MR950268
  21. [21] R.G. McLenaghan and T.G.C. Williams, An explicit determination of the Petrov type D space-times on which Weyl's neutrino equation and Maxwell's equations satisfy Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor.53 (1990) 217-223. Zbl0709.53053MR1079778
  22. [22] M.B. Monagan, K.O. Geddes, K.M. Heal, G. Labahn and S. Vorkoetter, Maple V Programming Guide, Springer, New York, 1996. 
  23. [23] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beit. zur Analysis18 (1981) 43-75. Zbl0501.53010MR650138
  24. [24] F.D. Sasse, Huygens' principle for relativistic wave equations on Petrov type III space-times, Ph.D. Thesis, University of Waterloo, 1997. 
  25. [25] T.F. Walton, The validity of Huygens' principle for the non-self-adjoint scalar wave equations on curved space-time, Master's Thesis, University of Waterloo, 1988. 
  26. [26] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen, Math. Nachr.47 (1970) 131-154. Zbl0211.40803MR298221
  27. [27] V. Wünsch, Huygens' principle on Petrov type D space-times, Ann. Physik46 (1989) 593-597. Zbl0697.53027MR1051239

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.