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Solutions globals d’équations du type Vlasov-Poisson. (Global solutions of Vlasov-Poisson type equations). (French) Zbl 0682.35022
Summary: This note is devoted to the study of Vlasov type equations in arbitrary dimensions. More precisely, in the case of Vlasov-Poisson equations, we give general results concerning the strong and weak stability of solutions, and the global existence of solutions. Our results include the repulsive case (electrostatic interactions) and the attractive case as well (gravitational interactions).

MSC:
35F25 Initial value problems for nonlinear first-order PDEs
35B35 Stability in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
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