×

Vlasov-Poisson-Fokker-Planck equation and stabilization system. (English) Zbl 1150.76566

Using the semi-group theory approach, the behavior of plasma and neutrons is described by a nonlinear Vlasov-Poisson-Fokker-Plank equation and a singular neutron transport equation, respectively. It is studied the problem to get stabilization of the plasma and neutrons near equilibriums. The main result asserts that the case of pure diffusion can be reached by using suitable adaptive control technique. Unfortunately, the corresponding proof is missing.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
93D15 Stabilization of systems by feedback
PDFBibTeX XMLCite