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On entropic solutions to conservation laws coupled with moving bottlenecks

T. Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. (2019)

Abstract. Moving bottlenecks in road traffic represent an interesting mathematical problem, which can be modeled via coupled PDE-ODE systems. We consider the case of a scalar conservation law modeling the evolution of vehicular traffic and an ODE with discontinuous right-hand side for the bottleneck. The bottleneck usually corresponds to a slow moving vehicle influencing the bulk traffic flow via a moving flux pointwise constraint. The definition of solutions requires a special entropy condition selecting nonclassical shocks and we prove existence of such solutions for initial data with bounded variation. Approximate solutions are constructed via the wave-front tracking method and their limit are solutions of the Cauchy problem PDE-ODE.

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Last updated on March 17, 2022

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Last Publications

Control of reaction-diffusion models in biology and social sciences

The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

Optimal actuator design via Brunovsky’s normal form

Turnpike in Optimal Control PDES, ResNets, and beyond

Local Stability and Convergence of Unconstrained Model Predictive Control

  • Control of reaction-diffusion models in biology and social sciences
  • DeustoCCMSeminar: Null controllability of a nonlinear age, space and two-sex structured population dynamics model
  • Optimal actuator design via Brunovsky’s normal form
  • Turnpike in Optimal Control PDES, ResNets, and beyond
  • Local Stability and Convergence of Unconstrained Model Predictive Control
  • Control of reaction-diffusion models in biology and social sciences
  • DeustoCCMSeminar: Null controllability of a nonlinear age, space and two-sex structured population dynamics model
  • Optimal actuator design via Brunovsky’s normal form
  • Turnpike in Optimal Control PDES, ResNets, and beyond
  • Local Stability and Convergence of Unconstrained Model Predictive Control
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