Dissertation/Thesis Abstract

Optimal Control of the Two-Dimensional Vlasov-Maxwell-System
by Weber, Jörg, M.Sc., Universitaet Bayreuth (Germany), 2018, 94; 27600460
Abstract (Summary)

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 inductors, 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 prove existence of a minimizer and deduce first order optimality conditions and the adjoint equation.

Indexing (document details)
School: Universitaet Bayreuth (Germany)
School Location: Germany
Source: DAI-C 81/4(E), Dissertation Abstracts International
Subjects: Mathematics
Publication Number: 27600460
ISBN: 9781687901101
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