TY - JOUR A1 - Gugat, Martin A1 - Ulbrich, Stefan ED - CHEN, GOONG T1 - The isothermal Euler equations for ideal gas with source term: Product solutions, flow reversal and no blow up JF - Journal of Mathematical Analysis and Applications KW - Global classical solutions Ideal gas Bi-directional flow Transsonic flow Y1 - 2017 U6 - https://doi.org/10.1016/j.jmaa.2017.04.064 VL - 454 IS - 1 SP - 439 EP - 452 ER - TY - JOUR A1 - Pfaff, Sebastian A1 - Ulbrich, Stefan T1 - Optimal Boundary Control of Nonlinear Hyperbolic Conservation Laws with Switched Boundary Data JF - SIAM Journal on Control and Optimization N2 - 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 C¹-functions at certain switching points and both the functions and the switching points are controlled. We show that the control-to-state mapping is differentiable in a certain generalized sense, which implies Fréchet-differentiability with respect to the control functions and the switching points for the composition with a tracking type functional, even in the presence of shocks. We also present an adjoint-based formula for the gradient of the reduced objective functional. KW - optimal control, scalar conservation law, differentiability, adjoint state, shock sensitivity Y1 - 2016 U6 - https://doi.org/10.1137/140995799 VL - 53 IS - 3 SP - 1250 EP - 1277 ER - TY - JOUR A1 - Pfaff, Sebastian A1 - Ulbrich, Stefan T1 - Optimal Control of Nonlinear Hyperbolic Conservation Laws by On/Off-Switching JF - Optimization Methods and Software N2 - This paper studies 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. The switching times between on-modes and off-modes are the control variables of the considered optimization problem, where a general tracking-type functional is minimized.We investigate the differentiability of the reduced objective function, also in the presence of shocks. We show that the state y(t,·) at some observation time t depends differentiably on the switching times in a generalized sense that implies total differentiability for the composition with a tracking functional. Furthermore, we present an adjoint-based formula for the gradient of the reduced objective functional with respect to the switching times. KW - optimal control, scalar conservation law, network Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2016.1236796 VL - 32 SP - 904 EP - 939 ER -