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On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field. (English) Zbl 1405.35214
Summary: The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global-in-time solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in finite time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.
35Q83 Vlasov equations
83F05 Relativistic cosmology
35Q76 Einstein equations
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
Full Text: DOI arXiv
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