Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times

W. G. Anderson; R. G. McLenaghan; F. D. Sasse

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

  • Volume: 70, Issue: 3, page 259-276
  • ISSN: 0246-0211

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Anderson, W. G., McLenaghan, R. G., and Sasse, F. D.. "Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times." Annales de l'I.H.P. Physique théorique 70.3 (1999): 259-276. <http://eudml.org/doc/76815>.

@article{Anderson1999,
author = {Anderson, W. G., McLenaghan, R. G., Sasse, F. D.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {scalar wave equation; Petrov type III space-times; Huygens' principle},
language = {eng},
number = {3},
pages = {259-276},
publisher = {Gauthier-Villars},
title = {Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times},
url = {http://eudml.org/doc/76815},
volume = {70},
year = {1999},
}

TY - JOUR
AU - Anderson, W. G.
AU - McLenaghan, R. G.
AU - Sasse, F. D.
TI - Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 70
IS - 3
SP - 259
EP - 276
LA - eng
KW - scalar wave equation; Petrov type III space-times; Huygens' principle
UR - http://eudml.org/doc/76815
ER -

References

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  1. [1] W. Anderson, Contributions to the study of Huygens' Principle for non-self-adjoint scalar wave equations on curved space-time, M. Math. Thesis, University of Waterloo, 1991. 
  2. [2] W.G. Anderson and R.G. Mclenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. - A sixth necessary condition, Ann. Inst. Henri Poincaré, Phys. Théor., 60, 1994, pp. 373-432. Zbl0806.35104MR1288586
  3. [3] W.G. Anderson, R.G. Mclenaghan and T.F. Walton, An explicit determination of the Non-self-adjoint wave equations that satisfy Huygens' principle on Petrov type III background space-times, Zeitschrift für Analysis und ihre Anwendungen - Journal for Analysis and its Applications, 16, 1996, pp. 37-58. Zbl0885.35062MR1453390
  4. [4] S.R. Czapor and R.G. Mclenaghan, NP: A Maple package for performing calculations in the Newman-Penrose formalism. Gen. Rel. Gravit., 19, 1987, pp. 623-635. Zbl0613.53033MR892637
  5. [5] S.R. Czapor, Gröbner Basis Methods for Solving Algebraic Equations, Research Report CS-89-51, 1989, Department of Computer Science, University of Waterloo, Ontario, Canada. Zbl1209.13002
  6. [6] 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, pp. 911-928. Zbl0758.53047MR1180241
  7. [7] 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, pp. 1-43. Zbl0046.32201MR50136
  8. [8] R.G. Mclenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditions, Ann. Inst. Henri Poincaré, A20, 1974, pp. 153-188. Zbl0287.35058MR361452
  9. [9] R.G. Mclenaghan, Huygens' principle, Ann. Inst. Henri Poincaré27, 1982, pp. 211-236. Zbl0528.35057MR694586
  10. [10] R.G. Mclenaghan and T.F. Walton, An explicit determination of the non-self-adjoint 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, pp. 267-280. Zbl0645.53047MR950268
  11. [11] 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 satisfiy Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor., 53, 1990, pp. 217-223. Zbl0709.53053MR1079778
  12. [12] 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, pp. 253-271. Zbl0869.53061MR1420704
  13. [13] E.T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys., 3, 1962, pp. 566-578. Zbl0108.40905MR141500
  14. [14] R. Penrose, A spinor approach to general relativity, Ann. Physics, 10, 1960, pp. 171-201. Zbl0091.21404MR115765
  15. [15] F.A.E. Pirani, in Lectures on General Relativity, S. Deser and W. Ford, ed., Prentice-Hall, New Jersey, 1964. 
  16. [16] F.D. Sasse, Huygens' Principle for Relativistic Wave Equations on Petrov type III Space-Times, Ph.D. Thesis, University of Waterloo, 1997. Zbl0885.53078
  17. [17] T.F. Walton, The validity of Huygens' Principle for the non-self-adjoint scalar wave equations on curved space-time, M. Math. Thesis, University of Waterloo, 1988. 
  18. [18] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen, Math. Nachr., 47, 1970, pp. 131-154. Zbl0211.40803MR298221
  19. [19] V. Wünsch, Huygens' principle on Petrov type D space-times, Ann. Physik, 46, 1989, pp. 593-597. Zbl0697.53027MR1051239

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