@article{AIHPA_1988__48_3_267_0, author = {McLenaghan, R. G. and Walton, T. F.}, title = {An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy {Huygens'} principle. {Part} {I} : {Petrov} type {N} background space-times}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {267--280}, publisher = {Gauthier-Villars}, volume = {48}, number = {3}, year = {1988}, mrnumber = {950268}, zbl = {0645.53047}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1988__48_3_267_0/} }
TY - JOUR AU - McLenaghan, R. G. AU - Walton, T. F. TI - An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times JO - Annales de l'I.H.P. Physique théorique PY - 1988 SP - 267 EP - 280 VL - 48 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1988__48_3_267_0/ LA - en ID - AIHPA_1988__48_3_267_0 ER -
%0 Journal Article %A McLenaghan, R. G. %A Walton, T. F. %T An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times %J Annales de l'I.H.P. Physique théorique %D 1988 %P 267-280 %V 48 %N 3 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1988__48_3_267_0/ %G en %F AIHPA_1988__48_3_267_0
McLenaghan, R. G.; Walton, T. F. An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times. Annales de l'I.H.P. Physique théorique, Volume 48 (1988) no. 3, pp. 267-280. http://archive.numdam.org/item/AIHPA_1988__48_3_267_0/
[1] Some hints on Huygens' principle and Hadamard's conjecture. Comm. Pure Appl. Math., t. 9, 1956, p. 307-326. | MR | Zbl
,[2] Some new results on the validity of Huygens' principle for the scalar wave equation on a curved space-time. Article in Gravitation. Geometry and Relativistic Physics, Proceedings of the Journées Relativistes 1984, Aussois, France, edited by Laboratoire Gravitation et Cosmologie Relativistes. Institut Henri Poincaré, Lecture Notes in Physics, t. 212, Springer-Verlag, Berlin, 1984. | MR | Zbl
and ,[3] 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., t. 44, 1986, p. 115-153. | Numdam | MR | Zbl
and ,[4] An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part II: Petrov type D space-times. Ann. Inst. Henri Poincaré, Phys. Théor., t. 47, 1987, p. 337-354. | Numdam | MR | Zbl
and ,[5] An explicit determination of the spacetimes on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III: Petrov type III space-times. Ann. Inst. Henri Poincaré, Phys. Théor., in press. | Numdam | Zbl
and ,[6] Le rayonnement gravitationnel : le tenseur de Riemann en relativité générale. Cah. Phys., t. 168-169, 1964, p. 303-349. | MR
,[7] Zur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus. S.-B. Sachs. Akad. Wiss. Leipzig Math.-Natur.,K., t. 100, 1952, p. 1-43. | MR | Zbl
,[8] Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103- 106. | MR | Zbl
,[9] Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven, 1923. | JFM
,[10] The problem of diffusion of waves. Ann. of Math., t. 43, 1942, p. 510-522. | MR | Zbl
,[11] Poissonsche Wellenformel in nichteuclidischen Räumen. Ber. Verh. Sachs. Akad. Wiss. Leipzig, t. 99, 1938, p. 55-66. | JFM | Zbl
,[12] Le problème de M. Hadamard relatif à la diffusion des ondes. Acta Math., t. 71, 1939, p. 249-282. | MR | Zbl
,[13] An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle. Proc. Cambridge Philos. Soc., t. 65, 1969, p. 139-155. | MR | Zbl
,[14] Complex recurrent spacetimes. Proc. Roy. Soc. London, t. A327, 1972, p. 229-249. | Zbl
McLENAGHAN and ,[15] 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, t. A20, 1974, p. 153-188. | Numdam | MR | Zbl
,[16] Huygens' principle. Ann. Inst. Henri Poincaré, t. A27, 1982, p. 211-236. | Numdam | MR | Zbl
,[17] An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys., t. 3, 1962, p. 566-578. | MR | Zbl
and ,[18] A spinor approach to general relativity. Ann. Physics, t. 10, 1960, p. 171-201. | MR | Zbl
,[19] Einstein-Raume. Academic Verlag, Berlin, 1964. | MR
,[20] Introduction to gravitational radiation theory. Article in Lectures on General Relativity, edited by S. Deser and W. Ford, Brandeis Summer Institute in Theoretical Physics, t. 1, 1964, Prentice-Hall, New York.
,[21] Zum Huygensschen Prinzip bei der skalaren Wellengleichung. Beitr. zur Analysis, t. 18, 1981, p. 43-75. | MR | Zbl
and ,[22] Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen. Math. Nachr., t. 47, 1970, p. 131-154. | MR | Zbl
,[23] Über eine Klasse Konforminvariater Tensoren. Math. Nach., t. 73, 1976, p. 37-58. | MR | Zbl
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