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Preprints, Working Papers, ... Year : 2023

Stabilization of conservation laws for G-solutions with application to traffic flow

Thibault Liard
  • Function : Author
Swann Marx
Vincent Perrollaz

Abstract

We address a problem of stabilization of a scalar conservation laws with fixed flux pointwise constraints. The PDE models the impact of two toll gates on the traffic flow and the feedback laws is designed to limit the number of cars passing through the two toll gates. The existence of solutions is proved using a Schauder’s fixed point theorem, together with a coupled PDEODE. To prove stabilization results, we study the structure of the solutions using an extension of backward generalized characteristics.
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Dates and versions

hal-04099345 , version 1 (16-05-2023)

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  • HAL Id : hal-04099345 , version 1

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Thibault Liard, Swann Marx, Vincent Perrollaz. Stabilization of conservation laws for G-solutions with application to traffic flow. 2023. ⟨hal-04099345⟩
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