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• W1509532272 abstract "This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic potential which leads to an additional state equation in form of a very weak elliptic PDE. Existence and uniqueness for the state equation is shown and the existence of a global optimal control is established. Moreover, first-order necessary optimality conditions in form of Karush-Kuhn-Tucker conditions are derived. A numerical test illustrates the theoretical findings." @default.
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• W1509532272 date "2014-11-26" @default.
• W1509532272 modified "2023-10-06" @default.
• W1509532272 title "Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations" @default.
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• W1509532272 doi "https://doi.org/10.48550/arxiv.1411.7265" @default.
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