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We consider optimal control problems governed by nonlinear hyperbolic conservation laws at junctions and analyze in particular the Fréchet-differentiability of the reduced objective functional. This is done by showing that the control-to-state mapping of the considered problems satisfies a generalized notion of differentiability. We consider both, the case… (More)

The Xenopus TFIIIA gene is transcribed very efficiently in oocytes. In addition to a TATA element at -30, we show that from -425 to +7 the TFIIIA gene contains only two positive cis elements centered at -267 (element 1) and -230 (element 2). This arrangement of the cis elements in the TFIIIA gene is striking because these two elements are positioned very… (More)

This paper focuses on the differentiability properties of the control-to-state mapping for entropy solutions to a scalar hyperbolic conservation law on R with respect to the switching times of an on/off control. As an example we consider the traffic density on a unidirectional road described by the LWR-model that is controlled by a traffic light switching… (More)

We consider the optimal control of initial-boundary value problems for entropy solutions of scalar hyperbolic conservation laws. In particular, we consider initial-boundary value problems where the initial and boundary data switch between different C 1-functions at certain switching points and both, the functions and the switching points, are controlled. We… (More)

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