Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||35|
|Published online||01 March 2021|
Optimal control of the two-dimensional Vlasov-Maxwell system
Department of Mathematics, University of Bayreuth,
* Corresponding author: Joerg.Weber@uni-bayreuth.de
Accepted: 15 October 2020
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 properly. 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.
Mathematics Subject Classification: 49J20 / 35Q61 / 35Q83 / 82D10
Key words: Relativistic Vlasov-Maxwell system / optimal control with PDE constraints / nonlinear partial differential equations / calculus of variations
© EDP Sciences, SMAI 2021
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