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Siberian Journal of Pure and Applied Mathematics, 2018, Volume 18, Issue 3, Pages 3–19
DOI: https://doi.org/10.33048/pam.2018.18.301 (Mi vngu474) 		 
Cauchy problem for a differential equation with piecewise smooth characteristics

D. S. Anikonovab, D. S. Konovalovaa

a Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk 630090, Russia
b Novosibirsk State University, 1, Pirogova St., Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/pam.2018.18.301
Abstract: The Cauchy problem is considered for an equation with first order partial derivatives and two independent variables. One of the coefficients multiplied by a partial derivative is assumed to be discontinuous. Therefore characteristics are proved to be piecewise smooth lines and hence the generalized solution of the Cauchy problem have specific properties. In particular, it is discontinuous in a certain domain and indefinite in another domain. Importance of such investigations is connected with possible applications of results in theory of probing.
Keywords: differential equations, Cauchy problem, discontinuous coefficients, existence, uniqueness, probing.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2015-001013-01-275
The work is supported by RAS presidium’s program (project No. 0314-2015-001013-01-275).
Received: 08.07.2017
English version:
Journal of Mathematical Sciences, 2021, Volume 253, Issue 3, Pages 339–353
DOI: https://doi.org/10.1007/s10958-021-05232-6
Document Type: Article
UDC: 517.958
Language: Russian
Citation: D. S. Anikonov, D. S. Konovalova, “Cauchy problem for a differential equation with piecewise smooth characteristics”, Sib. J. Pure and Appl. Math., 18:3 (2018), 3–19; J. Math. Sci., 253:3 (2021), 339–353
Citation in format AMSBIB
\Bibitem{AniKon18}
\by D.~S.~Anikonov, D.~S.~Konovalova
\paper Cauchy problem for a differential equation with piecewise smooth characteristics
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 3
\pages 3--19
\mathnet{http://mi.mathnet.ru/vngu474}
\crossref{https://doi.org/10.33048/pam.2018.18.301}
\transl
\jour J. Math. Sci.
\yr 2021
\vol 253
\issue 3
\pages 339--353
\crossref{https://doi.org/10.1007/s10958-021-05232-6}
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