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Related papers: Non-local traffic flow models with time delay: wel…

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We investigate a system describing the flow of a compressible two-component mixture. The system is composed of the compressible Navier-Stokes equations coupled with non-symmetric reaction-diffusion equations describing the evolution of…

Analysis of PDEs · Mathematics 2018-12-10 Tomasz Piasecki , Yoshihiro Shibata , Ewelina Zatorska

This paper deals with the one-dimensional formulation of Hughes model for pedestrian flows in the setting of entropy solutions, which authorizes non-classical shocks at the location of the so-called turning curve. We consider linear cost…

Analysis of PDEs · Mathematics 2021-07-22 Boris Andreianov , Massimiliano Rosini , Graziano Stivaletta

Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…

Numerical Analysis · Mathematics 2023-06-01 Raul Borsche , Axel Klar

We prove the existence of global weak entropy solutions for a class of non-symmetric Keyfitz-Kranzer type systems that includes lubrication models for thin-film flow. We identify a family of entropy/entropy-flux pairs for these first-order…

Analysis of PDEs · Mathematics 2026-04-20 Rahul Barthwal , Philipp Öffner , Christian Rohde

The paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring-road with possible nudging (or "look behind") terms. The obtained conditions are novel, as they are not…

Optimization and Control · Mathematics 2020-03-06 Iasson Karafyllis , Dionysis Theodosis , Markos Papageorgiou

We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…

Analysis of PDEs · Mathematics 2026-04-30 Mingwen Fei , Xiang Fei , Yadong Liu , Hao Wu

We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…

Numerical Analysis · Mathematics 2023-08-30 Dmitri Kuzmin , Mária Lukácova-Medvid'ová , Philipp Öffner

In this paper we investigate numerically the model for pedestrian traffic proposed in [B.Andreianov, C.Donadello, M.D.Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods…

Numerical Analysis · Mathematics 2015-03-11 Boris Andreianov , Carlotta Donadello , Ulrich Razafison , Massimiliano Daniele Rosini

We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…

Analysis of PDEs · Mathematics 2022-04-26 Tej-Eddine Ghoul , Nader Masmoudi , Eliot Pacherie

The ability to predict traffic flow over time for crowded areas during rush hours is increasingly important as it can help authorities make informed decisions for congestion mitigation or scheduling of infrastructure development in an area.…

Machine Learning · Computer Science 2023-04-03 Zann Koh , Yan Qin , Yong Liang Guan , Chau Yuen

We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…

Analysis of PDEs · Mathematics 2025-12-16 Antonin Chodron de Courcel

We propose a quantitative approach for calibrating and validating key features of traffic instabilities based on speed time series obtained from aggregated data of a series of neighboring stationary detectors. We apply the proposed criteria…

Physics and Society · Physics 2010-08-11 Martin Treiber , Arne Kesting

We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken…

Analysis of PDEs · Mathematics 2020-07-15 Xin Liu , Edriss S. Titi

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

Analysis of PDEs · Mathematics 2013-11-25 J. A. Carrillo , Y. -P. Choi , T. K. Karper

We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…

Analysis of PDEs · Mathematics 2018-09-11 Wen Shen

We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…

Numerical Analysis · Mathematics 2021-08-09 Andrea Bonito , Vivette Girault , Diane Guignard , Kumbakonam R. Rajagopal , Endre Süli

Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…

Numerical Analysis · Mathematics 2020-03-04 Yerlan Amanbek , Mary Wheeler

Inthispaper,weintroduceanon-localPDE-ODEtrafficmodeldevotedtothedescriptionof a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general…

Analysis of PDEs · Mathematics 2024-04-04 F. A. Chiarello , J. Friedrich , S. GÖttlich

In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…

Analysis of PDEs · Mathematics 2025-11-11 Marvin Fritz , Endre Süli , Barbara Wohlmuth

Precise and timely traffic flow prediction plays a critical role in developing intelligent transportation systems and has attracted considerable attention in recent decades. Despite the significant progress in this area brought by deep…

Machine Learning · Computer Science 2022-05-03 Wenzheng Zhao