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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Volume 21, Issue 3, Pages 317–325
DOI: https://doi.org/10.18500/1816-9791-2021-21-3-317-325
(Mi isu897)
 

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

Scientific Part
Mathematics

Solutions of the Loewner equation with combined driving functions

D. V. Prokhorov, A. M. Zakharov, A. V. Zherdev

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia
Full-text PDF (181 kB) Citations (1)
References:
Abstract: The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving functions and with combined constant and square root driving functions. In both cases, there is an analytical and geometrical description of generated traces. Earlier, Kager, Nienhuis and Kadanoff integrated the chordal Loewner differential equation either with a constant driving function or with a square root driving function. In the first case, the equation generates a rectilinear slit in the upper half-plane which is orthogonal to the real axis $\mathbb R$. In the second case, a rectilinear slit forms an angle to $\mathbb R$. In our paper, the multiple chordal Loewner differential equation generates more complicated hulls consisting of three rectilinear and curvilinear fragments which can be either intersecting or disjoint. Analytical results of the paper are accompanied by geometrical illustrations.
Key words: Loewner equation, driving function, trace, integrability case.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1399
This work was supported by the Program of development of Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies” (project No. 075-02-2021-1399).
Received: 22.03.2020
Accepted: 27.04.2021
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: English
Citation: D. V. Prokhorov, A. M. Zakharov, A. V. Zherdev, “Solutions of the Loewner equation with combined driving functions”, Izv. Saratov Univ. Math. Mech. Inform., 21:3 (2021), 317–325
Citation in format AMSBIB
\Bibitem{ProZahZhe21}
\by D.~V.~Prokhorov, A.~M.~Zakharov, A.~V.~Zherdev
\paper Solutions of the Loewner equation with combined driving functions
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2021
\vol 21
\issue 3
\pages 317--325
\mathnet{http://mi.mathnet.ru/isu897}
\crossref{https://doi.org/10.18500/1816-9791-2021-21-3-317-325}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000692198400004}
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  • https://www.mathnet.ru/eng/isu/v21/i3/p317
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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    Abstract page:137
    Full-text PDF :63
    References:25
     
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