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

Fabio Ancona; Annalisa Cesaroni; Giuseppe Maria Coclite; Mauro Garavello

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arXiv · 1803.07142

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

Fabio Ancona·Annalisa Cesaroni·Giuseppe Maria Coclite·Mauro Garavello

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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.

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Fabio Ancona, Annalisa Cesaroni, Giuseppe Maria Coclite, Mauro Garavello. 2018-03-19. On the optimization of conservation law models at a junction with inflow and flow distribution controls. https://arxiv.org/abs/1803.07142

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