no. 6
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, Tome 71 (1999) no. 6, pp. 595-620. 
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     title = {Complete solution of {Hadamard's} problem for the scalar wave equation on {Petrov} type {III} space-times},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {595--620},
     publisher = {Gauthier-Villars},
     volume = {71},
     number = {6},
     year = {1999},
     mrnumber = {1732144},
     zbl = {0951.35131},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1999__71_6_595_0/}
}
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Czapor, S. R.; McLenaghan, R. G.; 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, Tome 71 (1999) no. 6, pp. 595-620. http://www.numdam.org/item/AIHPA_1999__71_6_595_0/

[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. | EuDML | Numdam | MR | Zbl

[2] L. Asgeirsson, Some hints on Huygens' principle and Hadamard's conjecture, Comm. Pure Appl. Math. 9 (1956) 307-326. | MR | Zbl

[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. | MR

[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. | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[9] S.R. Czapor, Solving algebraic equations: Combining Buchberger's algorithm with multivariate factorization, J. Symbolic Comput. 7 (1989) 49-53. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[12] J.-C. Faugère, Résolution des systemes d'équation algébriques, Ph.D. Thesis, Université Paris, 1994.

[13] K.O. Geddes, S.R. Czapor and G. Labahn, Algorithms for Computer Algebra, Kluwer, Norwell, MA, 1992. | MR | Zbl

[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. | MR | Zbl

[15] J. Hadamard, Lectures on Cauchy's Problem in Linear Differential Equations, Yale University Press, New Haven, 1923. | JFM

[16] J. Hadamard, The problem of diffusion of waves, Ann. of Math. 35 (1942) 510- 522. | MR | Zbl

[17] M. Mathisson, Le probléme de M. Hadamard relatif à la diffusion des ondes, Acta Math. 71 (1939) 249-282. | MR | Zbl

[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). | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[22] M.B. Monagan, K.O. Geddes, K.M. Heal, G. Labahn and S. Vorkoetter, Maple V Programming Guide, Springer, New York, 1996.

[23] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beit. zur Analysis 18 (1981) 43-75. | MR | Zbl

[24] F.D. Sasse, Huygens' principle for relativistic wave equations on Petrov type III space-times, Ph.D. Thesis, University of Waterloo, 1997.

[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] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen, Math. Nachr. 47 (1970) 131-154. | MR | Zbl

[27] V. Wünsch, Huygens' principle on Petrov type D space-times, Ann. Physik 46 (1989) 593-597. | MR | Zbl