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We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open…

Numerical Analysis · Mathematics 2021-11-03 Harald Garcke , Robert Nürnberg

In this paper, a finite volume approximation scheme is used to solve a non-local macroscopic material flow model in two space dimensions, accounting for the presence of boundaries in the non-local terms. Based on a previous result for the…

Numerical Analysis · Mathematics 2025-10-21 Paola Goatin , Simone Göttlich , Fabian Ziegler

We prove the non-linear stability of a class of travelling-wave solutions to the extended Aw-Rascle system with a singular offset function, which is formally equivalent to the compressible pressureless Navier-Stokes system with a singular…

Analysis of PDEs · Mathematics 2024-04-29 Émile Deléage , Muhammed Ali Mehmood

We present a perturbation solution for a pressure-driven fluid flow in a rotating toroidal channel. The analysis shows the difference between the solutions of full and simplified equations studied earlier. The result is found to be reliable…

Fluid Dynamics · Physics 2009-11-13 A. Chupin , R. Stepanov

Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of model for calculating correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model…

Optimization and Control · Mathematics 2021-01-01 Ekaterina Kotliarova , Alexander Gasnikov , Evgenia Gasnikova , Demyan Yarmoshik

In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends…

Analysis of PDEs · Mathematics 2024-05-06 Abraham Sylla

The initial value problem to the multi-dimensional drift-flux model for two-phase flow is investigated in this paper, and the global existence of weak solutions with finite energy is established for general pressure-density functions…

Analysis of PDEs · Mathematics 2022-10-18 Hai-Liang Li , Ling-Yun Shou

We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can…

Analysis of PDEs · Mathematics 2019-02-22 Tokinaga Namba , Piotr Rybka , Vaughan Voller

Recent empirical studies have reported that spatiotemporal congestion clusters in urban traffic exhibit scale-free statistics, with cluster size following a power-law distribution. In this study, we address whether macroscopic continuum…

Physics and Society · Physics 2026-04-08 Yuki Chiba , Norikazu Saito , Yuki Ueda , Hiroaki Yoshida

In this paper, we address the problem of optimizing flows on generalized graphs that feature multiple entry points and multiple populations, each with varying cost structures. We tackle this problem by considering the multi-population…

Systems and Control · Electrical Eng. & Systems 2025-04-23 Tigran Bakaryan , Christoph Aoun , Ricardo de Lima Ribeiro , Naira Hovakimyan , Diogo Gomes

We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.

Analysis of PDEs · Mathematics 2010-12-15 Jun Kitagawa

We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a…

Analysis of PDEs · Mathematics 2017-12-20 Wen Shen , Karim Shikh-Khalil

Effects of large value assigned to the maximal car velocity on the fundamental diagrams in the Nagel-Schreckenberg model are studied by extended simulations. The function relating the flow in the congested traffic phase with the car density…

Physics and Society · Physics 2007-05-23 Danuta Makowiec , Wieslaw Miklaszewski

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

This paper focuses on the proof of the stability of entropy weak solutions of a nonlocal balance law modeling vehicular traffic flow on a road with on- and off-ramps. The stability is obtained with respect to a kernel function in the source…

Analysis of PDEs · Mathematics 2023-01-23 Felisia Angela Chiarello , Harold Deivi Contreras

We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…

Systems and Control · Computer Science 2015-05-25 Samuel Coogan , Murat Arcak

In this paper we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated…

Optimization and Control · Mathematics 2021-06-01 Meruza Kubentayeva , Alexander Gasnikov

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of…

Optimization and Control · Mathematics 2026-05-04 Eryn Vaid , Maria Teresa Chiri , Roberto Guglielmi , Gennaro Notomista

The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental diagram curves, each of which represents a class of drivers with a different empty road…

Physics and Society · Physics 2023-08-17 Shimao Fan , Michael Herty , Benjamin Seibold

The spatio-temporal structure of traffic flow pattern is investigated under the open boundary condition using the optimal velocity (OV) model. The parameter region where the uniform solution is convectively unstable is determined. It is…

Statistical Mechanics · Physics 2009-10-31 Namiko Mitarai , Hiizu Nakanishi