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First-order reduction and emergent behavior of the one-dimensional kinetic Cucker-Smale equation.
- Source :
-
Journal of Differential Equations . Nov2021, Vol. 302, p496-532. 37p. - Publication Year :
- 2021
-
Abstract
- In this paper, we introduce the kinetic description of the first-order Cucker-Smale (CS) flocking model on the real line. We reveal the equivalent relation between the measure-valued solution to the first- and second-order kinetic CS equations. The emergent behavior of the first-order kinetic CS equation and the characterization of the asymptotic solution are studied. We also provide the equivalent relation between classical/measure-valued solutions to the first-order kinetic CS equation and a classical solution to the second-order hydrodynamic CS equations, and present the corresponding analysis on the large-time behavior. The numerical experiments support our analysis and provide an efficient algorithm to obtain the asymptotic solution without simulating the model for a long time. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUATIONS
*ALGORITHMS
*BEHAVIORAL assessment
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 302
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 152739185
- Full Text :
- https://doi.org/10.1016/j.jde.2021.09.003