Well-posedness for scalar conservation laws with moving flux constraints
| Autor: | Thibault Liard, Benedetto Piccoli |
|---|---|
| Přispěvatelé: | Networked Controlled Systems (NECS), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Rutgers University [Camden], Rutgers University System (Rutgers) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Scalar (mathematics)
35L65 90B20 MathematicsofComputing_NUMERICALANALYSIS ComputerApplications_COMPUTERSINOTHERSYSTEMS 01 natural sciences backwards in time method Computer Science::Robotics Mathematics - Analysis of PDEs Wave-front tracking Scalar conservation laws with constraints ComputerApplications_MISCELLANEOUS ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Computer Science::Networking and Internet Architecture FOS: Mathematics Traffic flow modeling [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Tangent vector 0101 mathematics [MATH]Mathematics [math] Strongly coupled Physics Conservation law Applied Mathematics Mathematical analysis 010101 applied mathematics Mathematics::Differential Geometry Well posedness Tangent vectors Analysis of PDEs (math.AP) |
| Popis: | We consider a strongly coupled ODE-PDE system representing moving bottlenecks immersed in vehicular traffic. The PDE consists of a scalar conservation law modeling the traffic flow evolution and the ODE models the trajectory of a slow moving vehicle. The moving bottleneck influences the bulk traffic flow via a point flux constraint, which is given by an inequality on the flux at the slow vehicle position. We prove uniqueness and continuous dependence of solutions with respect to initial data of bounded variation. The proof is based on a new backward in time method established to capture the values of the norm of generalized tangent vectors at every time. 29 pages |
| Databáze: | OpenAIRE |
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