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Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 7, Pages 33–44 (Mi ivm9592)  

This article is cited in 1 scientific paper (total in 1 paper)

Existence of a solution to the Cauchy problem for the aggregation equation in hyperbolic space

V. F. Vil'danova

Bashkir State Pedagogical University of M. Akmulla, 3a Oktyabrskoj Revoljucii str., Ufa, 450008 Russia

Abstract: In hyperbolic space, we consider the Cauchy problem for the aggregation equation. Non-negative initial function limited and summable. The existence of a weak solution is proved on small time interval. In the case where the kernel of the integral operator is smooth and rapidly decreases at infinity, the existence of a bounded solution on an arbitrary interval of time is proved.

Keywords: the aggregation equation, solution existence, hyperbolic space.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00428_a


DOI: https://doi.org/10.26907/0021-3446-2020-7-33-44

Full text: PDF file (402 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:7, 27–37

Bibliographic databases:

UDC: 517.954
Received: 17.06.2019
Revised: 20.12.2019
Accepted: 25.03.2020

Citation: V. F. Vil'danova, “Existence of a solution to the Cauchy problem for the aggregation equation in hyperbolic space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 7, 33–44; Russian Math. (Iz. VUZ), 64:7 (2020), 27–37

Citation in format AMSBIB
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\by V.~F.~Vil'danova
\paper Existence of a solution to the Cauchy problem for the aggregation equation in hyperbolic space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 7
\pages 33--44
\mathnet{http://mi.mathnet.ru/ivm9592}
\crossref{https://doi.org/10.26907/0021-3446-2020-7-33-44}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 7
\pages 27--37
\crossref{https://doi.org/10.3103/S1066369X2007004X}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85089411615}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. F. Vildanova, “Edinstvennost resheniya zadachi Koshi dlya uravneniya agregatsii v giperbolicheskom prostranstve”, Izv. vuzov. Matem., 2021, no. 8, 27–36  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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