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Inverse Problem for a Nonlinear Wave Equation. / Romanov, V. G.; Bugueva, T. V.

In: Journal of Applied and Industrial Mathematics, Vol. 16, No. 2, 05.2022, p. 333-348.

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

Harvard

Romanov, VG & Bugueva, TV 2022, 'Inverse Problem for a Nonlinear Wave Equation', Journal of Applied and Industrial Mathematics, vol. 16, no. 2, pp. 333-348. https://doi.org/10.1134/S1990478922020132

APA

Romanov, V. G., & Bugueva, T. V. (2022). Inverse Problem for a Nonlinear Wave Equation. Journal of Applied and Industrial Mathematics, 16(2), 333-348. https://doi.org/10.1134/S1990478922020132

Vancouver

Romanov VG, Bugueva TV. Inverse Problem for a Nonlinear Wave Equation. Journal of Applied and Industrial Mathematics. 2022 May;16(2):333-348. doi: 10.1134/S1990478922020132

Author

Romanov, V. G. ; Bugueva, T. V. / Inverse Problem for a Nonlinear Wave Equation. In: Journal of Applied and Industrial Mathematics. 2022 ; Vol. 16, No. 2. pp. 333-348.

BibTeX

@article{438dd35bda074e8fbb2c92151691c6ce,
title = "Inverse Problem for a Nonlinear Wave Equation",
abstract = "We consider the inverse problem of determining the coefficient of the nonlinear term in anequation whose main part is the wave operator. The properties of the solution of the directproblem are studied; in particular, the existence and uniqueness of a bounded solution in aneighborhood of the characteristic cone is established, and the structure of this solution is writtenout. The problem of finding the unknown function is reduced to the problem of integral geometryon a family of straight lines with a weight function invariant with respect to rotations aroundsome fixed point. The uniqueness of the solution of the inverse problem is established, and analgorithm for reconstructing the desired function is proposed.",
keywords = "integral geometry, inverse problem, nonlinear wave equation",
author = "Romanov, {V. G.} and Bugueva, {T. V.}",
note = "Funding Information: This work was financially supported within the framework of the state order for the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0009. Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",
year = "2022",
month = may,
doi = "10.1134/S1990478922020132",
language = "English",
volume = "16",
pages = "333--348",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Inverse Problem for a Nonlinear Wave Equation

AU - Romanov, V. G.

AU - Bugueva, T. V.

N1 - Funding Information: This work was financially supported within the framework of the state order for the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0009. Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/5

Y1 - 2022/5

N2 - We consider the inverse problem of determining the coefficient of the nonlinear term in anequation whose main part is the wave operator. The properties of the solution of the directproblem are studied; in particular, the existence and uniqueness of a bounded solution in aneighborhood of the characteristic cone is established, and the structure of this solution is writtenout. The problem of finding the unknown function is reduced to the problem of integral geometryon a family of straight lines with a weight function invariant with respect to rotations aroundsome fixed point. The uniqueness of the solution of the inverse problem is established, and analgorithm for reconstructing the desired function is proposed.

AB - We consider the inverse problem of determining the coefficient of the nonlinear term in anequation whose main part is the wave operator. The properties of the solution of the directproblem are studied; in particular, the existence and uniqueness of a bounded solution in aneighborhood of the characteristic cone is established, and the structure of this solution is writtenout. The problem of finding the unknown function is reduced to the problem of integral geometryon a family of straight lines with a weight function invariant with respect to rotations aroundsome fixed point. The uniqueness of the solution of the inverse problem is established, and analgorithm for reconstructing the desired function is proposed.

KW - integral geometry

KW - inverse problem

KW - nonlinear wave equation

UR - http://www.scopus.com/inward/record.url?scp=85141917191&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/53a63bcf-9da0-3192-bc67-85ffec6e87c6/

U2 - 10.1134/S1990478922020132

DO - 10.1134/S1990478922020132

M3 - Article

AN - SCOPUS:85141917191

VL - 16

SP - 333

EP - 348

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 39523278