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2015 | 69 | 2 |
Tytuł artykułu

A continuum individual based model of fragmentation: dynamics of correlation functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on  Γ the Markov evolution of which is described in terms of their  correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.
Rocznik
Tom
69
Numer
2
Opis fizyczny
Daty
wydano
2015
online
2015-12-30
Twórcy
Bibliografia
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  • Finkelshtein, D., Around Ovsyannikov’s method, Methods Funct. Anal. Topology 21 (2) (2015), 134-150.
  • Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., Glauber dynamics in continuum: A constructive approach to evolution of states, Discrete Contin. Dyn. Syst. 33 (4) (2013), 1431-1450.
  • Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., Kutoviy, O., The statistical dynamics of a spatial logistic model and the related kinetic equation, Math. Models Methods Appl. Sci. 25 (2) (2015), 343-370.
  • Finkelshtein, D., Kondratiev, Y., Kutoviy, O., Individual based model with competition in spatial ecology, SIAM J. Math. Anal. 41 (2009), 297-317.
  • Finkelshtein, D., Kondratiev, Y., Oliveira, M. J., Markov evolution and hierarchical equations in the continuum. I: One-component systems, J. Evol. Equ. 9 (2009), 197-233.
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  • Kondratiev, Y., Kuna, T., Oliveira, M. J., Holomorphic Bogoliubov functionals for interacting particle systems in continuum, J. Funct. Anal. 238 (2006), 375-404.
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  • Kozitsky, Y., Dynamics of spatial logistic model: finite systems, in Banasiak, J., Bobrowski, A., Lachowicz, M. (eds.) Semigroups of Operators - Theory and Applications, Bedlewo, Poland, October 2013. Springer Proceedings in Mathematics & Statistics 113, 2015, 197-211.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_73-83
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