Characteristic initial value problem for hyperbolic systems of second order differential equations

 Access to full text

 Full (PDF)

1. [1] R.A. Adams, Sobolev Spaces, Academic Press, N. Y. 1975. Zbl0314.46030MR450957
2. [2] Choquet-Bruhat, CHRISTODOULOU and FRACOVILIA, Cauchy Data on a Manifold, Ann. Inst. Henri-Poincaré, 1978, Vol. XXIX. 
3. [3] Müller Zum Hagen and Seifert, Charakteristic and Mixed Problems, G.R.G. J., 1977, Vol. 8, pp. 259-301. Zbl0417.35052MR606056
4. [4] Christodoulou and Müller 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. Zbl0481.35059
5. [5] R. Courant and D. Hilber, Methods of Mathematical Physics, Vol. II, 9th printing, Interscience Publ. N.Y., 1962. Zbl0099.29504MR65391
6. [6] F.G. Friedlander, The Wave Equation of a Curved Space-Time, Cambridge University Press, 1975. Zbl0316.53021MR460898
7. [7] G.F.D. Duff, Mixed Problems for Linear Systems of First Order, Can. J. Math., 1958, Vol. 10, pp. 127-160. Zbl0080.07703MR97603
8. [8] J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, Berlin, Heidelbeg, New York, 1972. Zbl0223.35039MR350177
9. [9] I.P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Verlag Harri Deutsch, Zürich, Frankfurt/Main, Thun, 1977. Zbl0341.26003
10. [10] W. Rudin, Functional Analysis, McGraw-Hill Book Company, N.Y., 1973. Zbl0253.46001MR365062
11. [11] S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1973. Zbl0265.53054MR424186
12. [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. Zbl0442.35023MR576026
13. [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. MR616009
14. [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. MR345583
15. [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. MR1032984
16. [16] Y. Choquet-Bruhat, C. Dewitt-Morette and M. Dillard-Bleick, Analysis, Manifold and Physics, North Holland, Amsterdam, 1977. Zbl0385.58001MR467779
17. [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. MR797896
18. [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. Zbl0481.58026MR637872
19. [19] H. Friedrich, On Purely Radiative Space-Times, Commun. Math. Phys., 1986, Vol. 103, pp. 35-65. Zbl0584.53038MR826857
20. [20] J.M. Stewart, Classical General Relativity, W. B. BONNER, J. N. ISLAM, M. A. H. MAC CALLUM Eds., Cambridge University Press, 1984. MR779326
21. [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. Zbl0513.58043MR692204
22. [22] M. Dossa, Inegalités énergétiques sur un conoïde caractéristique. Annales de la Faculté des Sciences, Mathématiques-Physiques, 1985, T. 1, pp. 23-24. 
23. [23] F. Cagnac, Problème de Cauchy un conoide caractèristique pour des équations quasi linéaires, Anali Mat. Pura Appl., 1980, Vol. CXXIX, pp. 13-41. Zbl0486.35023MR648323
24. [24] G. Dautcourt, Zum charakteristischen Anfangswertproblem der Einsteinschen Feldgleichungen, Ann. Phys., 1963, Vol. 7, 12, pp. 302-323. Zbl0171.47301MR165949
25. [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. Zbl0588.35058MR806251
26. [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. Zbl0454.58017MR618984

1. Marcel Dossa, Espaces de Sobolev non isotropes, à poids et problèmes de Cauchy quasi-linéaires sur un conoïde caractéristique
2. Marcel Dossa, Solutions $C^{\infty }$ d’une classe de problèmes de Cauchy quasi-linéaires hyperboliques du second ordre sur un conoïde caractéristique