Blow-up for solutions of hyperbolic PDE and spacetime singularities

Journées équations aux dérivées partielles (2000), article no. 14, 12 p.

@incollection{JEDP_2000____A14_0, author = {Alan D. Rendall}, title = {Blow-up for solutions of hyperbolic {PDE} and spacetime singularities}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {14}, pages = {1--12}, publisher = {Universit\'e de Nantes}, year = {2000}, zbl = {01808704}, mrnumber = {2001j:58051}, language = {en}, url = {https://proceedings.centre-mersenne.org/item/JEDP_2000____A14_0/} }

TY - JOUR AU - Alan D. Rendall TI - Blow-up for solutions of hyperbolic PDE and spacetime singularities JO - Journées équations aux dérivées partielles PY - 2000 SP - 1 EP - 12 PB - Université de Nantes UR - https://proceedings.centre-mersenne.org/item/JEDP_2000____A14_0/ LA - en ID - JEDP_2000____A14_0 ER -

Alan D. Rendall. Blow-up for solutions of hyperbolic PDE and spacetime singularities. Journées équations aux dérivées partielles (2000), article no. 14, 12 p. https://proceedings.centre-mersenne.org/item/JEDP_2000____A14_0/

[1] Alinhac, S. 1995 Blowup for nonlinear hyperbolic equations. Birkhäuser, Boston. | MR | Zbl

[2] Andersson, L., Rendall, A. D. 2000 Quiescent cosmological singularities. Preprint gr-qc/0001047. | Zbl

[3] Belinskii, V.A., Khalatnikov, I.M. and Lifshitz, E.M. 1982 A general solution of the Einstein equations with a time singularity. Adv. Phys. 31, 639-667.

[4] Berger, B.K. 1997 Numerical investigation of singularities. In M. Francaviglia et. al. (eds.) Proceedings of the 14th International Conference on General Relativity and Gravitation. World Scientific, Singapore. | Zbl

[5] Chruściel, P. 1991 On uniqueness in the large of solutions of the Einstein equations («Strong Cosmic Censorship») Proc. CMA 27, ANU, Canberra. | MR | Zbl

[6] Friedrich, H., Rendall, A. D. 2000 The Cauchy problem for the Einstein equations. In B.G. Schmidt (ed) Einstein's Field Equations and Their Physical Implications. Lecture Notes in Physics 540. Springer, Berlin. | MR | Zbl

[7] Kichenassamy, S. and Littman, W. 1993 Blow-up surfaces for nonlinear wave equations I. Comm. PDE 18, 431-452. | MR | Zbl

[8] Kichenassamy, S. and Littman, W. 1993 Blow-up surfaces for nonlinear wave equations II. Comm. PDE 18, 1869-1899. | Zbl

[9] Kichenassamy, S. 1996 Fuchsian equations in Sobolev spaces and blow-up. J. Diff. Eq. 125, 299-327. | MR | Zbl

[10] Kichenassamy, S. 1996 The blow-up problem for exponential nonlinearities. Comm. PDE 21, 125-162. | MR | Zbl

[11] Kichenassamy, S. 1996 Nonlinear Wave Equations. Marcel Dekker, New York. | MR | Zbl

[12] Kichenassamy, S., Rendall, A. D. 1998 Analytic description of singularities in Gowdy spacetimes. Class. Quantum Grav. 15, 1339-1355. | Zbl

[13] Moncrief, V. 1980 Global properties of Gowdy spacetimes with T3 x R topology. Ann. Phys. (NY) 132, 87-107. | MR

[14] Montani, G. 1995 On the behaviour of the universe near the cosmological singularity. Class. Quantum Grav. 12, 2505-2517. | MR | Zbl

[15] Rendall, A. D. 2000 Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity. Preprint gr-qc/0004044. | MR | Zbl

[16] Ringström, H. 2000 Curvature blow-up in Bianchi VIII and IX vacuum spacetimes. Class. Quantum Grav. 17, 713-731. | MR | Zbl

[17] Weaver, M., Isenberg, J. and Berger, B.K. 1998 Mixmaster behavior in inhomogeneous cosmological spacetimes. Phys. Rev. Lett. 80, 2984-2987.