The Cucker-Smale equation: singular communication weight, measure-valued solutions and weak-atomic uniqueness
DOI10.1007/s00205-017-1160-xzbMath1384.35138arXiv1509.07673OpenAlexW2964034964MaRDI QIDQ1702439
Jan Peszek, Piotr Bogusław Mucha
Publication date: 28 February 2018
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1509.07673
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15) Weak solutions to PDEs (35D30) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05) Vlasov equations (35Q83) Pattern formations in context of PDEs (35B36)
Related Items (41)
Cites Work
- Unnamed Item
- On collision-avoiding initial configurations to Cucker-Smale type flocking models
- Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- A new model for self-organized dynamics and its flocking behavior
- A kinetic flocking model with diffusion
- Kinetic description of optimal control problems and applications to opinion consensus
- From particle to kinetic and hydrodynamic descriptions of flocking
- A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients
- Flocking with informed agents
- Kinetic models for the trading of goods
- A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
- Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system
- Sharp conditions to avoid collisions in singular Cucker-Smale interactions
- Macroscopic limit of self-driven particles with orientation interaction
- Flocking in noisy environments
- A CLASS OF INTERACTING PARTICLE SYSTEMS ON THE INFINITE CYLINDER WITH FLOCKING PHENOMENA
- EMERGENCE OF MULTI-CLUSTER CONFIGURATIONS FROM ATTRACTIVE AND REPULSIVE INTERACTIONS
- Heterophilious Dynamics Enhances Consensus
- A WELL-POSEDNESS THEORY IN MEASURES FOR SOME KINETIC MODELS OF COLLECTIVE MOTION
- Asymptotic Flocking Dynamics for the Kinetic Cucker–Smale Model
- SELF-PROPELLED INTERACTING PARTICLE SYSTEMS WITH ROOSTING FORCE
- Discrete Cucker--Smale Flocking Model with a Weakly Singular Weight
- Particle approximation of Vlasov equations with singular forces: Propagation of chaos
- Local well-posedness of the generalized Cucker-Smale model with singular kernels
- Cucker–Smale Flocking under Hierarchical Leadership
- CONTINUUM LIMIT OF SELF-DRIVEN PARTICLES WITH ORIENTATION INTERACTION
- Asymptotic dynamics for the Cucker–Smale-type model with the Rayleigh friction
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- Avoiding Collisions in Flocks
- Cucker-Smale Flocking With Inter-Particle Bonding Forces
- Stochastic flocking dynamics of the Cucker–Smale model with multiplicative white noises
- Emergent Behavior in Flocks
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