On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition
W. G. Anderson; R. G. McLenaghan
Annales de l'I.H.P. Physique théorique (1994)
- Volume: 60, Issue: 4, page 373-432
- ISSN: 0246-0211
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topAnderson, W. G., and McLenaghan, R. G.. "On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition." Annales de l'I.H.P. Physique théorique 60.4 (1994): 373-432. <http://eudml.org/doc/76640>.
@article{Anderson1994,
author = {Anderson, W. G., McLenaghan, R. G.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Huygens' principle; four independent variables},
language = {eng},
number = {4},
pages = {373-432},
publisher = {Gauthier-Villars},
title = {On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition},
url = {http://eudml.org/doc/76640},
volume = {60},
year = {1994},
}
TY - JOUR
AU - Anderson, W. G.
AU - McLenaghan, R. G.
TI - On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 4
SP - 373
EP - 432
LA - eng
KW - Huygens' principle; four independent variables
UR - http://eudml.org/doc/76640
ER -
References
top- [1] W.G. Anderson, Contributions to the Study of Huygens' Principle for the Non-self-adjoint Scalar Wave Equation on Curved Space-time, M. Math. Thesis (unpublished), University of Waterloo, 1991.
- [2] W.G. Anderson, R.G. McLenaghan and T.F. Walton, An Explicit Determination of the Non-Self-Adjoint Wave Equations on Curved Space-Time that Satisfy Huygens' Principle. Part II: Petrov Type III Background Space-Times, submitted to Ann. Inst. Henri Poincaré, Phys. Théor. Zbl0885.35062
- [3] W.G. Anderson and R.G. McLenaghan, On Huygens' Principle for Relativistic Wave Equations, C. R. Math. Rep. Acad. Sci. CanadaXV, 1993, p. 41. Zbl0765.35056MR1214215
- [4] L. Asgeirsson, Some Hints on Huygens' Principle and Hadamard's Conjecture, Comm. Pure Appl. Math., 9, 1956, p. 307. Zbl0074.31101MR82034
- [5] 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, p. 9. Zbl0729.35075
- [6] 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, p. 115. Zbl0595.35067MR839281
- [7] J. Carminati and R.G. McLenaghan, 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., 47, 1987, p. 337. Zbl0694.35074MR933681
- [8] J. Carminati and R.G. McLenaghan, An Explicit Determination of the 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, p. 77. Zbl0706.35131MR947160
- [9] J. Ehlers and K. Kundt, Exact Solutions of the Gravitational Field Equations, Chapter 2 of Gravitation an Introduction to Current Research, L. Witten editor, John Wiley and Sons, Toronto, 1962. MR143624
- [10] F.G. Friedlander, The Wave Equation on a Curved Space-Time, Cambridge University Press, London, 1976. Zbl0316.53021MR460898
- [11] P. Günther, Zur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus, S.-B. Sachs Akad. Wiss. Leipzig Math.-Natur. K., 100, 1952, p. 1. Zbl0046.32201MR50136
- [12] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differential-gleichungen mit vier unabhängigen Variablen, Arch. Ration. Mech. Anal., 18, 1965, p. 103. Zbl0125.05404MR174865
- [13] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip I, Math. Nach., 63, 1974, p. 97. Zbl0288.35042MR363377
- [14] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
- [15] J. Hadamard, The problem of diffusion of waves, Ann. Math., 43, 1942, p. 510. Zbl0063.01841MR6809
- [16] G. Herglotz, Uber die Bestimmung eines Linienelementes in normal Koordinaten aus dem Riemannschen Krümmgstensor, Math. Ann., 93, 1925, p. 46. MR1512221JFM50.0492.07
- [17] D. Lovelock, The Lanczos identity and its generalizations, Atti. Accad. Naz. Lincei, 42, 1967, p. 187. Zbl0194.22802MR216427
- [18] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes, Acad. Math., 71, 1939, p. 249. Zbl0022.22802MR728
- [19] R.G. McLenaghan, An Explicit Determination of the Empty Space-times on which the Wave Equation Satisfies Huygens' Principle, Proc. Cambridge Philos. Soc., 65, 1969, p. 139. Zbl0182.13403MR234700
- [20] R.G. McLenaghan, On the Validity of Huygen's Principle for Second Order Partial Differential Equations with four Independent Variables, Part I: Derivation of Necessary Conditions, Ann. Inst. Henri Poincaré, A20, 1974, p. 153. Zbl0287.35058MR361452
- [21] R.G. McLenaghan and T.F. Walton, 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, Ann. Inst. Henri Poincaré, Phys. Théor., 48, 1988, p. 267. Zbl0645.53047MR950268
- [22] R.G. McLenaghan and G.C. Williams, An Explicit Determination of the Petrov Type D Space-Times on which Weyl's Neutrino Equation and the Maxwell's Equations Satisfy Huygens' Principle, Ann. Inst. Henri Poincaré, Phys. Théor., 53, 1990, p. 217. Zbl0709.53053
- [23] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beitr. zur Analysis, 18, 1981, p. 43. Zbl0501.53010MR650138
- [24] K.L. Stellmacher, Ein Beispel einer Huygensschen Differentialgleichung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl., II, 10, 1953, p. 133. Zbl0052.09901MR60695
- [25] K.L. Stellmacher, Eine Klasse von Huygensschen Differentialgleichungen und ihre Integration, Math. Ann., 130, 1955, p. 219. Zbl0134.31101MR73831
- [26] V. Wünsch, Über selbstadjungiete Huygenssche Differentialglechungen mit vier unabhängen Variablen, Math. Nach., 47, 1970, p. 131. Zbl0211.40803MR298221
- [27] V. Wünsch, Maxwellsche Gleichungen und Huygensches Prinzip II. Math. Nach., 73, 1976, p. 19. Zbl0288.35043MR426807
- [28] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen-Klassen spinorieller Feldgleichungen II, Beitr. zur Analysis, 13, 1979, p. 147. Zbl0467.35067MR536225
- [29] V. Wünsch, Huygens' Principle on Petrov Type D Space-times, Ann. Physik., 46, 1989, p. 593. Zbl0697.53027MR1051239
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