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On the controllability of the Vlasov-Poisson system. (English) Zbl 1109.93007

Summary: We study the controllability of the Vlasov-Poisson system in a periodic domain, by means of an interior control located in an spatial subdomain. The first result proves the local exact zero controllability in the two-dimensional torus between two small acceptable distribution functions, with an arbitrary control zone. A second result establishes the global exact controllability in arbitrary dimension, provided the control zone satisfies the condition that it contains a hyperplane of the torus.

MSC:

93B05 Controllability
35B37 PDE in connection with control problems (MSC2000)
35F20 Nonlinear first-order PDEs
82D10 Statistical mechanics of plasmas
93C20 Control/observation systems governed by partial differential equations
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