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Solutions globales des équations d’Einstein-Maxwell

Julien Loizelet (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

En adaptant une méthode de Lindblad et Rodnianski, on prouve l’existence de solutions globales pour les équations d’Einstein-Maxwell en dimension d’espace n 3 . Les données initiales considérées sont lisses, asymptotiquement euclidiennes et suffisamment petites. On utilise la jauge harmonique et la jauge de Lorenz.

Solutions of a nonhyperbolic pair of balance laws

Michael Sever (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...

Solutions of a nonhyperbolic pair of balance laws

Michael Sever (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...

Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg–Landau equation

Leonid Berlyand, Volodymyr Rybalko (2010)

Journal of the European Mathematical Society

We study solutions of the 2D Ginzburg–Landau equation - Δ u + ε - 2 u ( | u | 2 - 1 ) = 0 subject to “semi-stiff” boundary conditions: Dirichlet conditions for the modulus, | u | = 1 , and homogeneous Neumann conditions for the phase. The principal result of this work shows that there are stable solutions of this problem with zeros (vortices), which are located near the boundary and have bounded energy in the limit of small ε . For the Dirichlet boundary condition (“stiff” problem), the existence of stable solutions with vortices, whose energy...

Currently displaying 101 – 120 of 349