# Blow-up for solutions of hyperbolic PDE and spacetime singularities

Journées équations aux dérivées partielles (2000)

- page 1-12
- ISSN: 0752-0360

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topRendall, Alan D.. "Blow-up for solutions of hyperbolic PDE and spacetime singularities." Journées équations aux dérivées partielles (2000): 1-12. <http://eudml.org/doc/93391>.

@article{Rendall2000,

abstract = {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.},

author = {Rendall, Alan D.},

journal = {Journées équations aux dérivées partielles},

keywords = {nonlinear hyperbolic systems},

language = {eng},

pages = {1-12},

publisher = {Université de Nantes},

title = {Blow-up for solutions of hyperbolic PDE and spacetime singularities},

url = {http://eudml.org/doc/93391},

year = {2000},

}

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

PB - Université de Nantes

SP - 1

EP - 12

AB - 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.

LA - eng

KW - nonlinear hyperbolic systems

UR - http://eudml.org/doc/93391

ER -

## References

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