Calculus of Variations and Geometric Measure Theory

F. Ancona - A. Cesaroni - G. M. Coclite - M. Garavello

On the optimization of conservation law models at a junction with inflow and flow distribution controls

created by cesaroni on 19 Mar 2018
modified on 01 Jul 2021


Published Paper

Inserted: 19 mar 2018
Last Updated: 1 jul 2021

Journal: SIAM J. Control Optim.
Volume: 56
Number: 5
Pages: 3370-3403
Year: 2018


The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely we consider a general class of junction distribution controls and inflow controls and we establish the compactness in $L^1$ of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edges.