PROPAGATION OF THE MONO-KINETIC SOLUTION IN THE CUCKER-SMALE-TYPE KINETIC EQUATIONS

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In this paper, we study the propagation of the mono-kinetic distribution in the CuckerSmale-type kinetic equations. More precisely, if the initial distribution is a Dirac mass for the variables other than the spatial variable, then we prove that this "mono-kinetic" structure propagates in time. For that, we first obtain the stability estimate of measure-valued solutions to the kinetic equation, by which we ensure the uniqueness of the mono-kinetic solution in the class of measure-valued solutions with compact supports. We then show that the mono-kinetic distribution is a special measure-valued solution. The uniqueness of the measure-valued solution implies the desired propagation of mono-kinetic structure.
Publisher
INT PRESS BOSTON, INC
Issue Date
2020-09
Language
English
Article Type
Article
Citation

COMMUNICATIONS IN MATHEMATICAL SCIENCES, v.18, no.5, pp.1221 - 1231

ISSN
1539-6746
DOI
10.4310/CMS.2020.V18.N5.A3
URI
http://hdl.handle.net/10203/276896
Appears in Collection
MA-Journal Papers(저널논문)
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