Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions

Berns C, Kondratiev Y, Kozitsky Y, Kutoviy O (2013)
Journal Of Dynamics And Differential Equations 25(4): 1027-1056.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Berns, ChristophUniBi; Kondratiev, YuriUniBi; Kozitsky, Yuri; Kutoviy, Oleksandr
Abstract / Bemerkung
The dynamics of an infinite system of point particles in R-d, which hop and interact with each other, is described at both micro- and mesoscopic levels. The states of the system are probability measures on the space of configurations of particles. For a bounded time interval , the evolution of states mu 0 bar right arrow mu(t) is shown to hold in a space of sub-Poissonian measures. This result is obtained by: (a) solving equations for correlation functions, which yields the evolution k(0) bar right arrow k(t), t is an element of {0, T) in a scale of Banach spaces; (b) proving that each is a correlation function for a unique measure mu(t). The mesoscopic theory is based on a Vlasov-type scaling, that yields a mean-field-like approximate description in terms of the particles' density which obeys a kinetic equation. The latter equation is rigorously derived from that for the correlation functions by the scaling procedure. We prove that the kinetic equation has a unique solution rho(t), t is an element of {0, +infinity).
Stichworte
Infinite particle system; Microscopic dynamics; Kinetic equation
Erscheinungsjahr
2013
Zeitschriftentitel
Journal Of Dynamics And Differential Equations
Band
25
Ausgabe
4
Seite(n)
1027-1056
ISSN
1040-7294
Page URI
https://pub.uni-bielefeld.de/record/2645270

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Berns C, Kondratiev Y, Kozitsky Y, Kutoviy O. Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions. Journal Of Dynamics And Differential Equations. 2013;25(4):1027-1056.
Berns, C., Kondratiev, Y., Kozitsky, Y., & Kutoviy, O. (2013). Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions. Journal Of Dynamics And Differential Equations, 25(4), 1027-1056. doi:10.1007/s10884-013-9328-z
Berns, C., Kondratiev, Y., Kozitsky, Y., and Kutoviy, O. (2013). Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions. Journal Of Dynamics And Differential Equations 25, 1027-1056.
Berns, C., et al., 2013. Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions. Journal Of Dynamics And Differential Equations, 25(4), p 1027-1056.
C. Berns, et al., “Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions”, Journal Of Dynamics And Differential Equations, vol. 25, 2013, pp. 1027-1056.
Berns, C., Kondratiev, Y., Kozitsky, Y., Kutoviy, O.: Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions. Journal Of Dynamics And Differential Equations. 25, 1027-1056 (2013).
Berns, Christoph, Kondratiev, Yuri, Kozitsky, Yuri, and Kutoviy, Oleksandr. “Kawasaki Dynamics in Continuum: Micro- and Mesoscopic Descriptions”. Journal Of Dynamics And Differential Equations 25.4 (2013): 1027-1056.

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