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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 1, Pages 3–24 (Mi izv317)  

This article is cited in 2 scientific papers (total in 2 papers)

Solubility of the transport equation in the kinetics of coagulation and fragmentation

P. B. Dubovski


Abstract: We prove a local existence theorem for a continuous solution of the spatially inhomogeneous kinetic coagulation-fragmentation model of Smoluchowski. Then we prove the solubility of the problem in the large in the class of continuous functions. It is important to emphasize that we admit unbounded integral kernels in both cases. The uniqueness of the solution and its continuous dependence on the input data are also demonstrated.

DOI: https://doi.org/10.4213/im317

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English version:
Izvestiya: Mathematics, 2001, 65:1, 1–22

Bibliographic databases:

MSC: 45K05, 82C22, 82C70, 35Q72
Received: 29.11.1999

Citation: P. B. Dubovski, “Solubility of the transport equation in the kinetics of coagulation and fragmentation”, Izv. RAN. Ser. Mat., 65:1 (2001), 3–24; Izv. Math., 65:1 (2001), 1–22

Citation in format AMSBIB
\Bibitem{Dub01}
\by P.~B.~Dubovski
\paper Solubility of the transport equation in the kinetics of coagulation and fragmentation
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 1
\pages 3--24
\mathnet{http://mi.mathnet.ru/izv317}
\crossref{https://doi.org/10.4213/im317}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1829401}
\zmath{https://zbmath.org/?q=an:1097.82024}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 1
\pages 1--22
\crossref{https://doi.org/10.1070/im2001v065n01ABEH000317}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747087768}


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  • https://doi.org/10.4213/im317
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Broizat D., “A kinetic model for coagulation-fragmentation”, Annales de l Institut Henri Poincare-Analyse Non Lineaire, 27:3 (2010), 809–836  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Meriem M., Aissaoui M.Z., Yashima H.F., “Stationary Solution to the Equation of Displacement and Coagulation of Droplets in a Vertical Wind”, Rev. Roum. Math. Pures Appl., 62:2 (2017), 309–338  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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