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- Title
Global existence and uniqueness of measure valued solutions to a Vlasov-type equation with local alignment.
- Authors
Gao, Yu; Xue, Xiaoping
- Abstract
We use a particle method to study a Vlasov-type equation with local alignment, which was proposed by Sebastien Motsch and Eitan Tadmor [ J. Statist. Phys., 141(2011), pp. 923-947]. For N-particle system, we study the unconditional flocking behavior for a weighted Motsch-Tadmor model and a model with a 'tail'. When N goes to infinity, global existence and stability (hence uniqueness) of measure valued solutions to the kinetic equation of this model are obtained. We also prove that measure valued solutions converge to a flock. The main tool we use in this paper is Monge-Kantorovich-Rubinstein distance.
- Subjects
VLASOV equation; KANTOROVICH method; PARTICLE methods (Numerical analysis); ASYMPTOTIC expansions; LYAPUNOV functions
- Publication
Mathematical Methods in the Applied Sciences, 2017, Vol 40, Issue 18, p7640
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4550