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Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients. / Anikonov, D. S.; Konovalova, D. S.

In: Journal of Mathematical Sciences (United States), Vol. 246, No. 6, 01.05.2020, p. 709-726.

Research output: Contribution to journal › Article › peer-review

Harvard

Anikonov, DS & Konovalova, DS 2020, 'Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients', Journal of Mathematical Sciences (United States), vol. 246, no. 6, pp. 709-726. https://doi.org/10.1007/s10958-020-04775-4

APA

Anikonov, D. S., & Konovalova, D. S. (2020). Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients. Journal of Mathematical Sciences (United States), 246(6), 709-726. https://doi.org/10.1007/s10958-020-04775-4

Vancouver

Anikonov DS, Konovalova DS. Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients. Journal of Mathematical Sciences (United States). 2020 May 1;246(6):709-726. doi: 10.1007/s10958-020-04775-4

Author

Anikonov, D. S. ; Konovalova, D. S. / Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients. In: Journal of Mathematical Sciences (United States). 2020 ; Vol. 246, No. 6. pp. 709-726.

BibTeX

@article{f8f6835897504b77920a912fdef171de,
title = "Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients",
abstract = "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.",
author = "Anikonov, {D. S.} and Konovalova, {D. S.}",
year = "2020",
month = may,
day = "1",
doi = "10.1007/s10958-020-04775-4",
language = "English",
volume = "246",
pages = "709--726",
journal = "Journal of Mathematical Sciences (United States)",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - Forward and Inverse Problems for Differential Equations with Discontinuous Coefficients

AU - Anikonov, D. S.

AU - Konovalova, D. S.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85084637698&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-04775-4

DO - 10.1007/s10958-020-04775-4

M3 - Article

AN - SCOPUS:85084637698

VL - 246

SP - 709

EP - 726

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 6

ER -

ID: 24313091