On an aggregation in birth-and-death stochastic dynamics

Finkelshtein D, Kondratiev Y, Kutoviy O, Zhizhina E (2014)
Nonlinearity 27(6): 1105-1133.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Finkelshtein, Dmitri; Kondratiev, YuriUniBi; Kutoviy, Oleksandr; Zhizhina, Elena
Abstract / Bemerkung
We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.
Stichworte
correlation functions; Markov evolutions in continuum; aggregation; non-local kinetic; mescoscopic scalings; equations
Erscheinungsjahr
2014
Zeitschriftentitel
Nonlinearity
Band
27
Ausgabe
6
Seite(n)
1105-1133
ISSN
0951-7715
Page URI
https://pub.uni-bielefeld.de/record/2685881

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Finkelshtein D, Kondratiev Y, Kutoviy O, Zhizhina E. On an aggregation in birth-and-death stochastic dynamics. Nonlinearity. 2014;27(6):1105-1133.
Finkelshtein, D., Kondratiev, Y., Kutoviy, O., & Zhizhina, E. (2014). On an aggregation in birth-and-death stochastic dynamics. Nonlinearity, 27(6), 1105-1133. doi:10.1088/0951-7715/27/6/1105
Finkelshtein, D., Kondratiev, Y., Kutoviy, O., and Zhizhina, E. (2014). On an aggregation in birth-and-death stochastic dynamics. Nonlinearity 27, 1105-1133.
Finkelshtein, D., et al., 2014. On an aggregation in birth-and-death stochastic dynamics. Nonlinearity, 27(6), p 1105-1133.
D. Finkelshtein, et al., “On an aggregation in birth-and-death stochastic dynamics”, Nonlinearity, vol. 27, 2014, pp. 1105-1133.
Finkelshtein, D., Kondratiev, Y., Kutoviy, O., Zhizhina, E.: On an aggregation in birth-and-death stochastic dynamics. Nonlinearity. 27, 1105-1133 (2014).
Finkelshtein, Dmitri, Kondratiev, Yuri, Kutoviy, Oleksandr, and Zhizhina, Elena. “On an aggregation in birth-and-death stochastic dynamics”. Nonlinearity 27.6 (2014): 1105-1133.