Characteristic initial value problem for hyperbolic systems of second order differential equations
Annales de l'I.H.P. Physique théorique, Tome 53 (1990) no. 2, pp. 159-216. 
@article{AIHPA_1990__53_2_159_0,
     author = {M\"uller zum Hagen, H.},
     title = {Characteristic initial value problem for hyperbolic systems of second order differential equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {159--216},
     publisher = {Gauthier-Villars},
     volume = {53},
     number = {2},
     year = {1990},
     mrnumber = {1079777},
     zbl = {0739.35039},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1990__53_2_159_0/}
}
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Müller zum Hagen, H. Characteristic initial value problem for hyperbolic systems of second order differential equations. Annales de l'I.H.P. Physique théorique, Tome 53 (1990) no. 2, pp. 159-216. http://archive.numdam.org/item/AIHPA_1990__53_2_159_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, N. Y. 1975. | MR | Zbl

[2] Choquet-Bruhat, CHRISTODOULOU and FRACOVILIA, Cauchy Data on a Manifold, Ann. Inst. Henri-Poincaré, 1978, Vol. XXIX.

[3] Müller Zum Hagen and Seifert, Charakteristic and Mixed Problems, G.R.G. J., 1977, Vol. 8, pp. 259-301. | MR | Zbl

[4] Christodoulou andMüller Zum Hagen, Extension de valeur initiale caractéristique pour des systèmes quasi linéaires de second ordre, C. R. Acad. Sci. Paris, 1981, T. 293, Series I, p. 39. | Zbl

[5] R. Courant and D. Hilber, Methods of Mathematical Physics, Vol. II, 9th printing, Interscience Publ. N.Y., 1962. | MR | Zbl

[6] F.G. Friedlander, The Wave Equation of a Curved Space-Time, Cambridge University Press, 1975. | MR | Zbl

[7] G.F.D. Duff, Mixed Problems for Linear Systems of First Order, Can. J. Math., 1958, Vol. 10, pp. 127-160. | MR | Zbl

[8] J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, Berlin, Heidelbeg, New York, 1972. | MR | Zbl

[9] I.P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Verlag Harri Deutsch, Zürich, Frankfurt/Main, Thun, 1977. | Zbl

[10] W. Rudin, Functional Analysis, McGraw-Hill Book Company, N.Y., 1973. | MR | Zbl

[11] S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1973. | MR | Zbl

[12] D. Christodoulou, Extension de la solution du problème de Cauchy d'équations quasi linéaires hyperboliques, C. R. Acad. Sci., Paris, 1980, T. 290, Series A, p. 641. | MR | Zbl

[13] D. Christodoulou, The Boost Problem for Weakly Coupled Quasilinear Hyperbolic System of the Second Order, preprint, Max-Planck-Institut für Physik und Astrophysik, MPI-PAE/Astro 218, 1980. | MR

[14] Müller Zum Hagen, Yodzis and Seifert, On the Occurrence of Naked Singularities, in Geneva/Relativity, Commun. Math. Phys., 1974, Vol. 37, pp. 29-40. | MR

[15] A.D. Rendall, Reduction of the Characteristic Initial Value Problem to the Cauchy Problem and its Application to Einstein Equations, Preprint, Max-Planck-Institut für Physik und Astrophysik, MPA 438, 1989. | MR

[16] Y. Choquet-Bruhat, C. Dewitt-Morette and M. Dillard-Bleick, Analysis, Manifold and Physics, North Holland, Amsterdam, 1977. | MR | Zbl

[17] G.F.R. Ellis, S.D. Nel, R. Maartens, W.R. Stoeger and A.P. Whitman, Phys. Rep., 1985, Vol. 124, pp. 315-417. | MR

[18] H. Friedrich, The Asymptotic Characteristic Initial Value Problem for Einstein's Vacuum Field Equations as an Initial Value Problem for First-Order Quasilinear Symmetric Hyperbolic System, Proc. R. Soc. Lond., 1981, Vol. A 378, pp. 401-421. | MR | Zbl

[19] H. Friedrich, On Purely Radiative Space-Times, Commun. Math. Phys., 1986, Vol. 103, pp. 35-65. | MR | Zbl

[20] J.M. Stewart, Classical General Relativity, W. B. BONNER, J. N. ISLAM, M. A. H. MAC CALLUM Eds., Cambridge University Press, 1984. | MR

[21] H. Friedrich and J. Stewart, Characteristic Initial Data and Wave Front Singularities in General Relativity, Proc. R. Soc. Lond., 1983, Vol. A 385, pp. 345-371. | MR | Zbl

[22] M. Dossa, Inegalités énergétiques sur un conoïde caractéristique. Annales de la Faculté des Sciences, Mathématiques-Physiques, 1985, T. 1, pp. 23-24.

[23] F. Cagnac, Problème de Cauchy un conoide caractèristique pour des équations quasi linéaires, Anali Mat. Pura Appl., 1980, Vol. CXXIX, pp. 13-41. | MR | Zbl

[24] G. Dautcourt, Zum charakteristischen Anfangswertproblem der Einsteinschen Feldgleichungen, Ann. Phys., 1963, Vol. 7, 12, pp. 302-323. | MR | Zbl

[25] H. Friedrich, On the Hyperbolicity of Einstein's and Other Gauge Field Equations, Commun. Math. Phy., 1985, Vol. 100, pp. 525-543; Proc. R. Soc. Lond., 1981, Vol. A 375, pp. 169-184. | MR | Zbl

[26] H. Friedrich, On the Regular and Assymptotic Characteristic Initial Value Problem for Einstein's Vacuum Field Equations, Proc. R. Soc. Lond., 1981, Vol. A 375, pp. 169- 184. | MR | Zbl