Abstract
Relativistic nonlinear wave propagation plays an important role in various areas of relativistic astrophysics and cosmology.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anile, A.M.: 1978, “Non-linear high-frequency waves in relativistic cosmology”, Atti Accad. Naz. Lincei, Rend. Ci. Sci. Fis. Mat. Nat., 63, 375.
Anile, A.M.: 1983a, “A geometric characterization of the compatibility relations for regularly discontinuous tensor field”, to be published in Le Matematiche.
Anile, A.M.: 1983b, “Evolution of shock waves in relativistic continuum mechanics”, to be published in Ann. Inst. Henri Poincaré.
Anile, A.M.: 1983c, “Propagation of weak shocks in relativistic fluid dynamics”, to be published in the Proceedings of the “Journées rélativistes”, Turin.
Anile, A.M. and Greco, A.: 1978, “Asymptotic waves and critical time in general relativistic magneto-hydrodynamics”, Ann. Inst. Henri Poincaré, 29,257.
Anile, A.M. and Greco, A.: 1979a, “Shock formation and shock structure in the cosmological radiative era”, Lett. Nuovo Cimento, 26, 121.
Anile, A.M. and Greco, A.: 1979b, “Non-linear wave propagation in a proton-electron plasma coupled with a strong radiation field”, Nuovo Cimento, 54, 307.
Anile, A.M. and Majorana, A.: 1981, “Shock structure for heat conducting and viscid fluids”, Meccanica, 2, 149.
Anile, A.M., Miller, J.C. and Motta, S.: 1980, “Damping of relativistic shocks, in annekpanding universe”, Lett. Nuovo Cimento, 29, 268.
Anile, A.M., Miller, J.C. and Motta, S.: 1983, “Formation and damping of relativistic strong shocks”, Phys. Fluids, 26, 1450.
Anile, A.M. and Muscato, O.: 1983, “Simple waves in relativistic magnetofluiddynamics”, to be published in Lett. Nuovo Cimento.
Bampi, F. and Morro, A.: 1980, “Two approaches to non-stationary relativistic thermodynamics”, J. Math. Phys., 21, 1201.
Barrow, J.: 1980, “Galaxy formation: the first million years”, Philos. Trans. R. Soc. London, A296, 273.
Blandford, R.D. and McKee, C.F.: 1976, “Fluid dynamics of relativistic blast waves”, Phys. Fluids, 19, 1130.
Bogoyavlenskii, O.I.: 1977, “General relativistic self-similar solution with a spherical shock wave”, Sov. Phys. JETP, 46, 633.
Boillat, G.: 1965, La propagation des ondes, Gauthier-Villars, Paris.
Boillat, G.: 1975, “Chocs caractéristiques et ondes simple exceptionelles pour les systèmes conservatifs à intégrale d’énergie: forme explicite de la solutions”, C.R. Seances Acad. Sci. Paris, 280A, 1325.
Boillat, G.: 1982, “Urti”, in Ferrarese (ed.), Wave propagation , Liguori, Napoli.
Cahill, M.E. and Taub, A.H.: 1971, “Spherically symmetric similarity solutions of the Einstein field equations for a perfect fluid”, Commun. Math. Phys., 21, 1.
Cattaneo, C.: 1948, “Sulla conduzione del calore”, Atti Semin. Mat. Fis. Univ. Modena, 3, 83.
Chapline, G.F. and Weaver, T.A.: 1979, “Structure of relativistic shock waves in simple gases”, Phys. Fluids, 22, 1885.
Chen, P.J.: 1976, Selected topics in wave propagation, Noordhoff, Leyden.
Chevalier, R.A.: 1981, “Hydrodynamic models of supernova explosions”, Fundamentals of cosmic physics, 7, 1.
Choquet-Bruhat, Y.: 1969, “Ondes asymptotiques et approchées pour des systèmes d’équations aux dérivées partielles non linéaires”, J. Math. Pures et Appl., 48, 117.
Choquet-Bruhat, Y.: 1982, “Ondes asymptotiques”, in Ferrarese (ed.), Wave propagation, Liguori, Napoli.
De Groot, S.R., Vande Leeuwen, W.A. and Van Weert, Ch.G.: 1980, Relativistio kinetic theory, North Holland, Amsterdam.
Dixon, G.: 1978, Special Relativity, the foundation of macroscopic physics, Cambridge University Press, Cambridge.
Eckhoff, K.: 1981, “On stability for symmetric hyperbolic systems, I”, J. Differ. Equations, 40, 94.
Friedlander, F.G.: 1975, The wave equation on a curved space-time, Cambridge University Press, Cambridge.
Gilbard, D. and Paolucci, D.: 1953, “The structure of shock waves in the continuum theory of fluids”, J. Rat. Mech. An., 2, 617.
Gross, R.A.: 1971, “The physics of strong shock waves in gases”, in P. Caldirola and H. Knoepfel, (ed.), Physics of High Energy density, Academic Press Inc., New York.
Ikeuchi, S., Tomisaka, K. and Ostriker, J.: 1983, “The structure and expansion law of a shock wave in an expanding universe”, Astrophys. J., 265, 583.
Israel, W.: 1976, “Nonstationary irreversible thermodynamics: a causal relativistic theory”, Ann. Rhys. (USA), 100, 310.
Israel, W. and Stewart, J.: 1979, “On transient relativistic thermodynamics and kinetic theory”, Rroc. R. Soc., London, A365, 43.
Jeffrey, A.: 1976, Quasilinear hyperbolic systems and waves, Pitman, London.
Jones, B.J.T.: 1971, “The origin and evolution of structure in the Universe”, unpublished Ph. D. Thesis, Cambridge.
Jones, B.J.T.: 1976, “The origin of galaxies: A review of recent theoretical developments and their confrontation with observation”, Rev. Mod. Phys., 48, 107.
Kline, M. and Kay, I.: 1965, Electromagnetic theory and Geometrical Optics, J. Wiley and Sons, New York.
Koch, P.A.: 1965, “Relativistic shock structure”, Phys. Rev., A140, 1161.
Lanza, A., Miller, J.C. and Motta, S.: 1982, “Relativistic shocks in a Synge gas”, Lett. Nuovo Cimento, 35, 309.
Landau, L.D. and Lifshitz, E.M.: 1959, Fluid Mechanics, Pergamon Press, London.
Lanza, A., Miller, J.C. and Motta, S.: 1983, “Relativistic shock waves in a Synge gas”, preprint, University of Catania.
Liang, E.P.T.: 1977a, “Relativistic simple waves: shock damping and entropy production”, Astrophys. J., 211, 361.
Liang, E.P.T.: 1977b, “Galaxies and entropy from nonlinear fluctuations: a simple waves analysis”, Astrophys. J., 216, 206.
Liang, E.P.T. and Baker, K.: 1977, “Damping of relativistic shocks”, Phys. Rev. Lett., 39, 191.
Lichnerowicz, A.: 1971, “Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magneto-hydrodynamique relativistes”, in C. Cattaneo (éd.), Relativistic fluid dynamics, Cremonese, Roma.
Lichnerowicz, A.: 1975, “Ondes de choc gravitationelles et ondes de choc mangétomatérielles extrêmes”, C.R. Seances Acad. Sci. Paris, 281, 929.
Lindblom, L. and Hiscock, A.A.: 1983, “On the stability of rotating stellar models in general relativity theory”, Astrophys. J., 267, 384.
Ludwig, D.: 1966, “Uniform asymptotic expansion at a caustic”, Commun. Pure Appl. Math., 19, 215.
MacCallum, M.A.H., and Taub, A.H.: 1973, “The averaged lagrangian and high-frequency gravitational waves”, Commun. Math. Phys., 30, 153.
Maugin, G.: 1976, “Conditions de compatibilité pour une hypersurface singulière en mécanique relativiste des milieux continus”, Ann. Inst. Henri Poincaré, 24, 213.
Modugno, M. and Stefani, G.: 1979, “On the geometrical structure of shock waves in general relativity”, Ann. Inst. Henri Poincaré, 30, 27.
Müller, I.: 1967, “Zum Paradoxon der Wärmeleitungstheorie”, Z. Phys., 198, 329.
Müller, I. and Liu, I.: 1983, “Extended thermodynamics of classical and degenerate ideal gases”, preprint, University of Berlin.
Peebles, P.J.E.: 1970, “Non linear limit on primeval adiabatic perturbations”, Phys. Rev., D1, 397.
Peebles, P.J.E.: 1980, The large-scale structure of the universe, Princeton University Press, Princeton.
Ruggeri, T. and Strumia, A.: 1981, “Main field and convex covariant density for quasi-linear hyperbolic systems”, Ann. Inst. Henri Poincaré, 34, 65.
Schmidt, B.: 1964, “Electron beam density measurement in shock waves in argon”, J. Fluid Mech., 39,361.
Serrin, P.: 1959, “Mathematical principles of Classical fluid mechanics”, in Handbuck der Physik, VIII/1, Springer-Verlag, New York.
Taub, A.H.: 1948, “Relativistic Rankine-Hugoniot equations”, Phys. Rev.,74, 328.
Taub, A.H.: 1978, “Relativistic fluid mechanics”, Annu. Rev. Fluid Mech., 10, 301.
Taussig, R.: 1973, “Shock wave production of relativistic plasmas”, in M.J. Lighthill, I. Imai and H. Sato (eds), Dynamics of ionized gases, University of Tokyo Press, Tokyo.
Van Riper, K.A.: 1979, “General relativistic hydrodynamics and the adiabatic collapse of stellar cores”, Astrophys. J.,232, 558.
Vishniac, E.T.: 1982, “Nonlinear effects on cosmological perturbations. I. The evolution of adiabatic perturbations”, Astrophys. J., 253, 446.
Whitham, G.B.: 1974, Linear and nonlinear waves, J. Wiley and Sons, New York.
Zeldovich, Y.B. and Novikov, I.D.s 1982, Struttura ed evoluzione dell’Universo, (Italian edition), Editori Riuniti, Roma.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D. Reidel Publishing Company
About this chapter
Cite this chapter
Anile, A.M. (1984). Nonlinear Wave Propagation in Relativistic Hydrodynamics and Cosmology. In: Bertotti, B., de Felice, F., Pascolini, A. (eds) General Relativity and Gravitation. Fundamental Theories of Physics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6469-3_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-6469-3_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6471-6
Online ISBN: 978-94-009-6469-3
eBook Packages: Springer Book Archive