Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients

Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients Full article

Journal

Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795

Output data

Year: 2020, Volume: 246, Number: 6, Pages: 709-726 Pages count : 18 DOI: 10.1007/s10958-020-04775-4

Authors

Anikonov D.S. ^1,2 , Konovalova D.S. ¹

Affiliations

1	Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, 1, Pirogova St, Novosibirsk, 630090, Russian Federation

We study the Cauchy problem for an almost linear first order differential equation with discontinuous coefficient of the time-derivative. We analyze differential properties of a weak solution to the forward problem and study the inverse problem of finding the discontinuity lines for the time-independent coefficient. For this purpose the trace of a solution to the Cauchy problem is assumed to be given on a plane far from the line in question. We develop an algorithm for solving the inverse problem. Our study can be considered as a fragment of the theory of probing inhomogeneous media by physical signals. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Anikonov D.S. , Konovalova D.S.
Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients
Journal of Mathematical Sciences (United States). 2020. V.246. N6. P.709-726. DOI: 10.1007/s10958-020-04775-4 Scopus OpenAlex

Scopus:	2-s2.0-85084637698
OpenAlex:	W3014546406

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