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Siberian Journal of Pure and Applied Mathematics, 2018, Volume 18, Issue 2, Pages 13–29
DOI: https://doi.org/10.17377/PAM.2018.18.3
(Mi vngu469)
 

Forward and inverse problems with discontinuous coefficient

D. S. Anikonovab, D. S. Konovalovab

a Novosibirsk State University, 1, Pirogova St., Novosibirsk 630090, Russia
b Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk 630090, Russia
References:
Abstract: We consider an almost linear differential equation with discontinuous coefficient with respect to the derivative on time. The Cauchy problem is stated and investigated. The inverse problem is stated after studding differential properties of a generalized solution for the forward problem. In the inverse problem we look for a line where the coefficients are discontinuous is sought for. Additionally, the solution of the forward problem is given on a certain plane outside the line. The main result of the article is an algorithm for solving the inverse problem. This investigation may be treated as a part of the theory of probing heterogeneous media by physical signals.
Keywords: differential equations, Cauchy problem, discontinuous coefficients, existence, uniqueness, inverse problems, 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: 29.03.2017
English version:
Journal of Mathematical Sciences, 2020, Volume 246, Issue 6, Pages 709–726
DOI: https://doi.org/10.1007/s10958-020-04775-4
Document Type: Article
UDC: 517.958
Language: Russian
Citation: D. S. Anikonov, D. S. Konovalova, “Forward and inverse problems with discontinuous coefficient”, Sib. J. Pure and Appl. Math., 18:2 (2018), 13–29; J. Math. Sci., 246:6 (2020), 709–726
Citation in format AMSBIB
\Bibitem{AniKon18}
\by D.~S.~Anikonov, D.~S.~Konovalova
\paper Forward and inverse problems with discontinuous coefficient
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 2
\pages 13--29
\mathnet{http://mi.mathnet.ru/vngu469}
\crossref{https://doi.org/10.17377/PAM.2018.18.3}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 246
\issue 6
\pages 709--726
\crossref{https://doi.org/10.1007/s10958-020-04775-4}
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