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

2018/03/19 by Ancona, Fabio, Cesaroni, Annalisa, Coclite, Giuseppe Maria +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.07142

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 L¹ 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.

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• On the structure of optimal solutions of conservation laws at a junction with one incoming and one outgoing arc

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