# 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 21 Jul 2018

[BibTeX]

Submitted Paper

Inserted: 19 mar 2018
Last Updated: 21 jul 2018

Year: 2018

Abstract:

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.