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Related papers: Discrete Cucker-Smale's flocking model with a weak…

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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

In this paper, we study a continuous ocking Cucker-Smale model with noise, which has isotropic and polarized stationary solutions depending on the intensity of the noise. The first result establishes the threshold value of the noise…

Analysis of PDEs · Mathematics 2024-05-13 Xingyu Li

A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic…

Analysis of PDEs · Mathematics 2022-12-06 Li Chen , Yue Li , Nicola Zamponi

We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…

Optimization and Control · Mathematics 2017-10-04 Christoforos Somarakis , Evripidis Paraskevas , John S. Baras , Nader Motee

The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that…

Analysis of PDEs · Mathematics 2025-10-01 Maria Heitzinger , Ansgar Jüngel

We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…

Analysis of PDEs · Mathematics 2020-03-18 Giovanni Paolo Galdi , Václav Mácha , Šárka Nečasová

The study of collective behavior in multi-agent systems has attracted the attention of many researchers due to its wide range of applications. Among them, the Cucker-Smale model was developed to study the phenomenon of flocking, and various…

Dynamical Systems · Mathematics 2023-08-31 Jong-Ho Kim , Young Ju Lee , Jea-Hyun Park

The Motsch-Tadmor (MT) model is a variant of the Cucker-Smale model with a normalized communication weight function. The normalization poses technical challenges in analyzing the collective behavior due to the absence of conservation of…

Numerical Analysis · Mathematics 2024-08-21 Seung-Yeal Ha , Franca Hoffmann , Dohyeon Kim , Wook Yoon

We present an emergent stochastic flocking dynamics of the Cucker-Smale (CS) ensemble under randomly switching topologies. The evolution of the CS ensemble with randomly switching topologies involves two random components (switching times…

Optimization and Control · Mathematics 2019-11-19 Jiu-Gang Dong , Seung-Yeal Ha , Jinwook Jung , Doheon Kim

A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…

Analysis of PDEs · Mathematics 2018-05-28 Prasanta Kumar Barik , Ankik Kumar Giri

In this paper, we consider the Cucker-Smale flocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a "non flocking" to a "flocking" state as the…

Analysis of PDEs · Mathematics 2017-11-29 Young-Pil Choi , Samir Salem

We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities together with a continuity argument, we…

Dynamical Systems · Mathematics 2017-12-05 Young-Pil Choi , Zhuchun Li

In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the…

Analysis of PDEs · Mathematics 2025-03-18 Shenglun Yan , Weiyuan Zou

In this paper, we deal with a Cucker-Smale model with time-dependent time delay and communication failures. Namely, we investigate the situation in which the agents involved in a flocking process can possibly suspend the exchange of…

Optimization and Control · Mathematics 2025-08-19 Elisa Continelli

In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. Here, we consider the critical case…

Analysis of PDEs · Mathematics 2021-05-26 Daniel Lear

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

Numerical Analysis · Mathematics 2025-10-09 Juan Vicente Gutiérrez-Santacreu

We prove existence and uniqueness of strong solutions to the Cucker--Smale flocking model coupled with an incompressible viscous non-Newtonian fluid, with the stress tensor of a power--law structure for $p\geq\frac{11}{5}$. The coupling is…

Analysis of PDEs · Mathematics 2017-02-24 Piotr B. Mucha , Jan Peszek , Milan Pokorny

We discuss the Cucker-Smale's (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S…

Analysis of PDEs · Mathematics 2008-06-16 Seung-Yeal Ha , Eitan Tadmor

We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…

Analysis of PDEs · Mathematics 2019-05-22 Javier Morales , Jan Peszek , Eitan Tadmor

We consider the following Keller-Segel system of degenerate type: \partial u / \partial t = \partial / \partial x (\partial u^m / \partial x - u^{q-1} \cdot \partial v / \partial x), x \in \R, t>0, \partial^2 v / \partial x^2 - \gamma v +…

Analysis of PDEs · Mathematics 2009-02-12 Yoshie Sugiyama