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On the dynamical collapse of pseudo-relativistic quantum stars. (Sur l’effondrement dynamique des étoiles quantiques pseudo-relativistes.) (French) Zbl 1325.35229

Summary: Dans cet exposé, je présente plusieurs modèles quantiques non linéaires permettant de décrire certaines étoiles. Je m’intéresse tout particulièrement à l’effondrement gravitationnel des étoiles trop lourdes, un phénomène modélisé par des solutions qui explosent en temps fini. Je montre l’existence de telles solutions et je décris plusieurs de leurs propriétés au temps d’explosion.

MSC:

35Q85 PDEs in connection with astronomy and astrophysics
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
85A05 Galactic and stellar dynamics
85A15 Galactic and stellar structure
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