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2016 | 70 | 1 |
Tytuł artykułu

A kinetic equation for repulsive coalescing random jumps in continuum

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of solutions of the corresponding kinetic equation are proved.
Rocznik
Tom
70
Numer
1
Opis fizyczny
Daty
wydano
2016
online
2016-07-04
Twórcy
Bibliografia
  • Aldous, D. J., Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists, Bernoulli 5 (1) (1999), 3-48.
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  • Banasiak, J., Lamb, W., Langer, M., Strong fragmentation and coagulation with power-law rates, J. Engrg. Math. 82 (2013), 199-215.
  • Belavkin, V. P., Kolokoltsov, V. N., On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 459 (2031) (2003), 727-748.
  • Berns, C., Kondratiev, Y., Kozitsky, Y., Kutoviy, O., Kawasaki dynamics in continuum: micro- and mesoscopic descriptions, J. Dynam. Differential Equations 25 (4) (2013), 1027-1056.
  • Capitan, J. A., Delius, G. W., Scale-invariant model of marine population dynamics, Phys. Rev. E (3) 81 (6) (2010), 061901, 15pp.
  • 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., Vlasov scaling for stochastic dynamics of continuous systems, J. Stat. Phys. 141 (1) (2010), 158-178.
  • Finkelshtein, D., Kondratiev, Y., Kutoviy, O., Statistical dynamics of continuous systems: perturbative and approximative approaches, Arabian Journal of Mathematics 4 (4) (2015), 255-300.
  • Finkelshtein, D., Kondratiev, Y., Joao Oliveira, M., Markov evolutions and hierarchical equations in the continuum. I. One-component systems, J. Evol. Equ. 9 (2) (2009), 197-233.
  • Kolokoltsov, V. N., Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles, J. Statist. Phys. 115 (5-6) (2004), 1621-1653.
  • Kondratiev, Y., Kuna, T., Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5(2) (2002), 201-233.
  • Lachowicz, M., Laurencot, P., Wrzosek, D., On the Oort-Hulst-Safronov coagulation equation and its relation to the Smoluchowski equation, SIAM J. Math. Anal. 34 (6) (2003), 1399-1421 (electronic).
  • Lamb, W., Applying functional analytic techniques to evolution equations, in Evolutionary Equations with Applications in Natural Sciences, volume 2126 of Lecture Notes in Math., 1-46, Springer, Cham, 2015.
  • Rudnicki, R., Wieczorek, R., Fragmentation-coagulation models of phytoplankton, Bull. Pol. Acad. Sci. Math. 54 (2) (2006), 175-191.
  • Rudnicki, R., Wieczorek, R., Phytoplankton dynamics: from the behaviour of cells to a transport equation, Math. Model. Nat. Phenom. 1 (1) (2006), 83-100.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2016_70_1_47
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