A kinetic equation for repulsive coalescing random jumps in continuum

Krzysztof Pilorz

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2016)

  • Volume: 70, Issue: 1
  • ISSN: 0365-1029

Abstract

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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.

How to cite

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Krzysztof Pilorz. "A kinetic equation for repulsive coalescing random jumps in continuum." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 70.1 (2016): null. <http://eudml.org/doc/289804>.

@article{KrzysztofPilorz2016,
abstract = {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.},
author = {Krzysztof Pilorz},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Coalescence; coagulation; hopping particles; individual-based model; configuration spaces; infinite particle system; microscopic dynamics; Vlasov scaling; kinetic equation},
language = {eng},
number = {1},
pages = {null},
title = {A kinetic equation for repulsive coalescing random jumps in continuum},
url = {http://eudml.org/doc/289804},
volume = {70},
year = {2016},
}

TY - JOUR
AU - Krzysztof Pilorz
TI - A kinetic equation for repulsive coalescing random jumps in continuum
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2016
VL - 70
IS - 1
SP - null
AB - 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.
LA - eng
KW - Coalescence; coagulation; hopping particles; individual-based model; configuration spaces; infinite particle system; microscopic dynamics; Vlasov scaling; kinetic equation
UR - http://eudml.org/doc/289804
ER -

References

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  2. Banasiak, J., Kinetic models in natural sciences, in Evolutionary Equations with Applications in Natural Sciences, volume 2126 of Lecture Notes in Math., 133-198, Springer, Cham, 2015. 
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  8. Finkelshtein, D., Kondratiev, Y., Kutoviy, O., Vlasov scaling for stochastic dynamics of continuous systems, J. Stat. Phys. 141 (1) (2010), 158-178. 
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  10. 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. 
  11. Kolokoltsov, V. N., Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles, J. Statist. Phys. 115 (5-6) (2004), 1621-1653. 
  12. Kondratiev, Y., Kuna, T., Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5(2) (2002), 201-233. 
  13. 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). 
  14. 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. 
  15. Rudnicki, R., Wieczorek, R., Fragmentation-coagulation models of phytoplankton, Bull. Pol. Acad. Sci. Math. 54 (2) (2006), 175-191. 
  16. Rudnicki, R., Wieczorek, R., Phytoplankton dynamics: from the behaviour of cells to a transport equation, Math. Model. Nat. Phenom. 1 (1) (2006), 83-100. 

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