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An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that of constructing large families of solutions of the Einstein equations with singularities of a simple type by solving singular hyperbolic systems. Heuristic considerations indicate, however, that the generic case will be much more complicated and require different techniques.
@incollection{JEDP_2000____A14_0,
author = {Rendall, Alan D.},
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},
doi = {10.5802/jedp.578},
mrnumber = {2001j:58051},
zbl = {01808704},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.578/}
}
TY - JOUR AU - Rendall, Alan D. 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 - http://geodesic.mathdoc.fr/articles/10.5802/jedp.578/ DO - 10.5802/jedp.578 LA - en ID - JEDP_2000____A14_0 ER -
%0 Journal Article %A Rendall, Alan D. %T Blow-up for solutions of hyperbolic PDE and spacetime singularities %J Journées équations aux dérivées partielles %D 2000 %P 1-12 %I Université de Nantes %U http://geodesic.mathdoc.fr/articles/10.5802/jedp.578/ %R 10.5802/jedp.578 %G en %F JEDP_2000____A14_0
Rendall, Alan D. Blow-up for solutions of hyperbolic PDE and spacetime singularities. Journées équations aux dérivées partielles (2000), article no. 14, 12 p.. doi: 10.5802/jedp.578
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