TY - INPR A1 - Gugat, Martin A1 - Sokolowski, Jan T1 - On Problems of Dynamic Optimal Nodal control for Gas Networks N2 - We consider a dynamic ptimal control problem for gas pipeline systems. The flow is governed by a quasilinear hyperbolic model. Since in the operation of the gas networks regular solutions without shocks are desirable, we impose appropriate state and control constraint in order to guarantee that a classical solution is generated. Due to a W^{2;inf}-regularization term in the objective function, we can show the existence of an optimal control. Moreover, we give conditions that guarantee that the control becomes constant a the end of the control time interval if the weight of the regularization term is suffciently large. KW - optimal nodal control KW - gas network KW - turnpike property KW - quasilinear hyperbolic problem KW - dynamic control Y1 - 2021 ER - TY - JOUR A1 - Gugat, Martin A1 - Keimer, Alexander A1 - Leugering, Günter A1 - Wang, Zhiqiang ED - Piccoli, Benedetto T1 - Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks JF -  Networks and Heterogeneous Media N2 - We consider a system of scalar nonlocal conservation laws on networks that model a highly re-entrant multi-commodity manufacturing system as encountered in semiconductor production. Every single commodity is mod-eled by a nonlocal conservation law, and the corresponding PDEs are coupled via a collective load, the work in progress. We illustrate the dynamics for two commodities. In the applications, directed acyclic networks naturally occur, therefore this type of networks is considered. On every edge of the network we have a system of coupled conservation laws with nonlocal velocity. At the junctions the right hand side boundary data of the foregoing edges is passed as left hand side boundary data to the following edges and PDEs. For distributing junctions, where we have more than one outgoing edge, we impose time dependent distribution functions that guarantee conservation of mass. We provide results of regularity, existence and well-posedness of the multi-commodity network model for L p-, BV-and W 1,p-data. Moreover, we define an L 2-tracking type objective and show the existence of minimizers that solve the corresponding optimal control problem. KW - conservation laws on network KW - nonlocal conservation laws KW - optimal nodal control KW - systems of hyperbolic pdes Y1 - 2016 U6 - https://doi.org/DOI: 10.3934/nhm.2015.10.749 VL - 10 IS - 4 SP - 749 EP - 785 ER -