Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads

DOI10.3934/nhm.2019028zbMath1437.65111arXiv1809.02998OpenAlexW2980787919MaRDI QIDQ2303651

Wen Shen

Publication date: 4 March 2020

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02998

zbMATH Keywords

traveling wavesintegro-differential equationtraffic flowrough coefficientconservation laws with nonlocal flux

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) PDEs with low regular coefficients and/or low regular data (35R05) Traffic problems in operations research (90B20) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Computational methods for problems pertaining to operations research and mathematical programming (90-08) Traveling wave solutions (35C07) Integro-partial differential equations (35R09) First-order hyperbolic equations (35L02) PDEs in connection with mathematical programming (35Q90)

Related Items (9)

Wavefronts in traffic flows and crowds dynamics ⋮ Modeling Multilane Traffic with Moving Obstacles by Nonlocal Balance Laws ⋮ On traffic flow with nonlocal flux: a relaxation representation ⋮ Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux ⋮ Convergence of a second-order scheme for non-local conservation laws ⋮ A space-time nonlocal traffic flow model: relaxation representation and local limit ⋮ Nonlocal scalar conservation laws with discontinuous flux ⋮ Stationary wave profiles for nonlocal particle models of traffic flow on rough roads ⋮ Systems of conservation laws with discontinuous fluxes and applications to traffic

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