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Generalized solutions of the Vlasov-Poisson system with singular data. (English) Zbl 1132.35337

Summary: We study spherically symmetric solutions of the Vlasov-Poisson system in the context of algebras of generalized functions. This allows to model highly concentrated initial configurations and provides a consistent setting for studying singular limits of the system. The proof of unique solvability in our approach depends on new stability properties of the system with respect to perturbations.

MSC:

35F20 Nonlinear first-order PDEs
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
35Q60 PDEs in connection with optics and electromagnetic theory
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