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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 neural transport for normalizing flows

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

Gaussian Beam ansatz for finite difference wave equations

Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave

Optimal design of sensors via geometric criteria

  • Control of neural transport for normalizing flows
  • A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
  • Gaussian Beam ansatz for finite difference wave equations
  • Optimal design of sensors via geometric criteria
  • Eigenvalue bounds for the Gramian operator of the heat equation
  • Control of neural transport for normalizing flows
  • A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation
  • Gaussian Beam ansatz for finite difference wave equations
  • Optimal design of sensors via geometric criteria
  • Eigenvalue bounds for the Gramian operator of the heat equation
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