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- W2892412534 abstract "The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of the problem since existence of global, classical solutions of the full three-dimensional problem is not known. We add external currents to the system, in applications generated by coils, to control the plasma in a proper way. After considering global existence of solutions to this system, differentiability of the control-to-state operator is proved. In applications, on the one hand, we want the shape of the plasma to be close to some desired shape. On the other hand, a cost term penalizing the external currents shall be as small as possible. These two aims lead to minimizing some objective function. We restrict ourselves to only such control currents that are realizable in applications. After that, we prove existence of a minimizer and deduce first order optimality conditions and the adjoint equation." @default.
- W2892412534 created "2018-10-05" @default.
- W2892412534 creator A5037652732 @default.
- W2892412534 date "2021-01-01" @default.
- W2892412534 modified "2023-09-25" @default.
- W2892412534 title "Optimal control of the two-dimensional Vlasov-Maxwell system" @default.
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- W2892412534 doi "https://doi.org/10.1051/cocv/2020069" @default.
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