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Izvestiya: Mathematics, 2017, Volume 81, Issue 1, Pages 99–136
DOI: https://doi.org/10.1070/IM8401 (Mi im8401) 		 
This article is cited in 13 scientific papers (total in 13 papers)

On the theory of the Frankl problem for equations of mixed type

K. B. Sabitovab

a Institute of Applied Research, Sterlitamak
b Sterlitamak Branch of Bashkir State University
English version PDF (560 kB) Citations (13) Russian version article
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DOI: https://doi.org/10.1070/IM8401
Abstract: In 1956 Frankl, while studying subsonic flows past a profile with a supersonic zone terminating with a normal compression shock, arrived at a new mathematical problem for the Chaplygin equation with a non-local boundary condition. In this article we give a survey of classical and recent papers dedicated to this problem. We present theorems on the existence and uniqueness of the solution of the Frankl problem, study the spectral problem for the Lavrent'ev–Bitsadze operator, show applications of these results to the construction of a solution with the aid of a series, and state some unsolved problems.
Keywords: equation of mixed type, Frankl problem, survey, uniqueness, existence, Frankl spectral problem, eigenfunctions, completeness, basis property.
Received: 27.04.2015
Revised: 14.08.2015
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35M12, 35P10, 35C10, 76G25
Language: English
Original paper language: Russian
Citation: K. B. Sabitov, “On the theory of the Frankl problem for equations of mixed type”, Izv. Math., 81:1 (2017), 99–136
Citation in format AMSBIB
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\by K.~B.~Sabitov
\paper On the theory of the Frankl problem for equations of mixed type
\jour Izv. Math.
\yr 2017
\vol 81
\issue 1
\pages 99--136
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  • https://doi.org/10.1070/IM8401
  • https://www.mathnet.ru/eng/im/v81/i1/p101
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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