Global existence and uniqueness of measure valued solutions to a vlasov-type equation with local alignment

Yu Gao; Xiaoping Xue

doi:10.1002/mma.4550

Global existence and uniqueness of measure valued solutions to a vlasov-type equation with local alignment

Yu Gao, Xiaoping Xue

Department of Applied Mathematics

Research output: Journal article publication › Journal article › Academic research › peer-review

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.

Original language	English
Pages (from-to)	7640-7662
Number of pages	23
Journal	Mathematical Methods in the Applied Sciences
Volume	40
Issue number	18
DOIs	https://doi.org/10.1002/mma.4550
Publication status	Published - Dec 2017

Keywords

Flocking
Monge-Kantorovich-Rubinstein distance
Particle method

ASJC Scopus subject areas

General Mathematics
General Engineering

More information

10.1002/mma.4550

Cite this

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title = "Global existence and uniqueness of measure valued solutions to a vlasov-type equation with local alignment",

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.",

keywords = "Flocking, Monge-Kantorovich-Rubinstein distance, Particle method",

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note = "Funding Information: We would like to thank the support by the National Science Foundation of China under grants 11671109 and 11401135. Funding Information: National Science Foundation of China, Grant/Award Number: 11671109, 11401135 Publisher Copyright: {\textcopyright} 2017 John Wiley & Sons, Ltd.",

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AU - Gao, Yu

AU - Xue, Xiaoping

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PY - 2017/12

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N2 - 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.

AB - 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.

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KW - Particle method

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Global existence and uniqueness of measure valued solutions to a vlasov-type equation with local alignment

Abstract

Keywords

ASJC Scopus subject areas

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