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Author: Hintermüller, Michael × End date: 2022 × DDC: 510 × Has files: Yes × Type: Text × Subject: boundary control ×

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    Constrained exact boundary controllability of a semilinear model for pipeline gas flow
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Gugat, Martin; Habermann, Jens; Hintermüller, Michael; Huber, Olivier
    While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.
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    Differentiability properties for boundary control of fluid-structure interactions of linear elasticity with Navier--Stokes equations with mixed-boundary conditions in a channel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Hintermüller, Michael; Kröner, Axel
    In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generaziling the results of [Wollner and Wick, J. Math. Fluid Mech., 21, 2019] to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners.