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Related papers: Non-local dissipative Aw-Rascle model and its rela…

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In this paper, we study a nonlocal extension of the Aw-Rascle-Zhang traffic model, where the pressure-like term is modeled as a convolution between vehicle density and a kernel function. This formulation captures nonlocal driver…

Analysis of PDEs · Mathematics 2026-02-10 Debora Amadori , Felisia Angela Chiarello , Gianmarco Cipollone

We study the multi-dimensional Euler-alignment system with a matrix-valued communication kernel, motivated by models of anticipation dynamics in collective behaviour. A key feature of this system is its formal equivalence to a nonlocal…

Analysis of PDEs · Mathematics 2025-11-10 Jakub Woźnicki , Ewelina Zatorska

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a…

Analysis of PDEs · Mathematics 2022-08-05 Nilasis Chaudhuri , Eduard Feireisl , Ewelina Zatorska

We discuss a nonlocal version of the Generalized Aw-Rascle-Zhang model, a second-order vehicular traffic model where the empty road velocity is a Lagrangian marker governed by a transport equation. The evolution of the car density is…

Analysis of PDEs · Mathematics 2025-05-16 Elio Marconi , Laura V. Spinolo

We study the derivation of second order macroscopic traffic models from kinetic descriptions. In particular, we recover the celebrated Aw-Rascle model as the hydrodynamic limit of an Enskog-type kinetic equation out of a precise…

Statistical Mechanics · Physics 2020-01-24 Giacomo Dimarco , Andrea Tosin

We investigate the large-time behavior of the pressureless Euler system with nonlocal velocity alignment and interaction forces, with the aim of characterizing the asymptotic convergence of classical solutions under general interaction…

Analysis of PDEs · Mathematics 2025-10-29 José A. Carrillo , Young-Pil Choi , Dowan Koo , Oliver Tse

We study the validity of the dissipative Aw-Rascle system as a macroscopic model for pedestrian dynamics. The model uses a congestion term (a singular diffusion term) to enforce capacity constraints in the crowd density while inducing a…

Physics and Society · Physics 2024-02-02 Pedro Aceves-Sanchez , Rafael Bailo , Pierre Degond , Zoe Mercier

We study the Aw-Rascle system in a one-dimensional domain with periodic boundary conditions, where the offset function is replaced by the gradient of the function $\rho_{n}^{\gamma}$, where $\gamma \to \infty$. The resulting system…

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

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For an arbitrary large class of initial data and the periodic domain, we prove the existence of global-in-time measure-valued solutions.…

Analysis of PDEs · Mathematics 2023-02-24 Nilasis Chaudhuri , Piotr Gwiazda , Ewelina Zatorska

We study a pressureless Euler system with a nonlinear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density…

Analysis of PDEs · Mathematics 2017-11-22 Tam Do , Alexander Kiselev , Lenya Ryzhik , Changhui Tan

We introduce the notion of duality solution for the hard-congestion model on the real line, and additionally prove an existence result for this class of solutions. Our study revolves around the analysis of a generalised Aw-Rascle system,…

Analysis of PDEs · Mathematics 2024-02-14 Nilasis Chaudhuri , Muhammed Ali Mehmood , Charlotte Perrin , Ewelina Zatorska

We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…

Analysis of PDEs · Mathematics 2007-12-27 Jerry L. Bona , David Lannes , Jean-Claude Saut

We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler…

Analysis of PDEs · Mathematics 2017-07-18 Young-Pil Choi , Jan Haskovec

We investigate the pressureless fractional Euler-alignment system with nonlinear velocity couplings, referred to as the $p$-Euler-alignment system. This model features a nonlinear velocity alignment force, interpreted as a density-weighted…

Analysis of PDEs · Mathematics 2024-09-17 Young-Pil Choi , Michał Fabisiak , Jan Peszek

In this study, we analyse the famous Aw-Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the…

Analysis of PDEs · Mathematics 2022-09-27 N Chaudhuri , L Navoret , Charlotte Perrin , E Zatorska

We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…

Machine Learning · Statistics 2025-11-17 Inga Girshfeld , Xiaohui Chen

We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment…

Analysis of PDEs · Mathematics 2021-06-16 José A. Carrillo , Young-Pil Choi

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…

Analysis of PDEs · Mathematics 2024-07-02 Timothée Crin-Barat , Yue-Jun Peng , Ling-Yun Shou , Jiang Xu

The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…

Analysis of PDEs · Mathematics 2017-01-16 M. Bostan , J. A. Carrillo

This is a continuation of our previous joint work on the $\st$-model in[\textit{Well-posedness and long time behavior of the Euler Alignment System with adaptive communication strength}, accepted at the Abel Symposium Proceedings, also…

Analysis of PDEs · Mathematics 2025-03-27 Roman Shvydkoy , Trevor Teolis
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