Hyperbolic methods for Einstein's equations.
Reula, Oscar A. (1998)
Living Reviews in Relativity [electronic only]
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Reula, Oscar A. (1998)
Living Reviews in Relativity [electronic only]
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Kentaro Saji, Handan Yıldırım (2015)
Annales Polonici Mathematici
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We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the...
Walid Ben Youssef, Thierry Colin (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type. ...
Yvonne Choquet-Bruhat, James York (1997)
Banach Center Publications
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We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.
Jawher El Goul (1996)
Manuscripta mathematica
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Sudhanshu K. Ghoshal, Abha Ghoshal, M. Abu-Masood (1977)
Annales Polonici Mathematici
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Romanov, V. G. (2003)
Sibirskij Matematicheskij Zhurnal
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H. Komatsu (1980-1981)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Avalishvili, G., Gordeziani, D. (1999)
Bulletin of TICMI
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J. Kisyński (1970)
Colloquium Mathematicae
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Michał Kisielewicz (1975)
Annales Polonici Mathematici
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Duong Trong Luyen, Nguyen Minh Tri (2016)
Annales Polonici Mathematici
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The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator with a locally Lipschitz nonlinearity satisfying a subcritical growth condition.