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Inverse Problem for the Wave Equation with a Polynomial Nonlinearity. / Romanov, V. G.; Bugueva, T. V.

In: Journal of Applied and Industrial Mathematics, Vol. 17, No. 1, 03.2023, p. 163-167.

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

Harvard

Romanov, VG & Bugueva, TV 2023, 'Inverse Problem for the Wave Equation with a Polynomial Nonlinearity', Journal of Applied and Industrial Mathematics, vol. 17, no. 1, pp. 163-167. https://doi.org/10.1134/s1990478923010180

APA

Romanov, V. G., & Bugueva, T. V. (2023). Inverse Problem for the Wave Equation with a Polynomial Nonlinearity. Journal of Applied and Industrial Mathematics, 17(1), 163-167. https://doi.org/10.1134/s1990478923010180

Vancouver

Romanov VG, Bugueva TV. Inverse Problem for the Wave Equation with a Polynomial Nonlinearity. Journal of Applied and Industrial Mathematics. 2023 Mar;17(1):163-167. doi: 10.1134/s1990478923010180

Author

Romanov, V. G. ; Bugueva, T. V. / Inverse Problem for the Wave Equation with a Polynomial Nonlinearity. In: Journal of Applied and Industrial Mathematics. 2023 ; Vol. 17, No. 1. pp. 163-167.

BibTeX

@article{75530dfcecea43d4856076a233d4407b,
title = "Inverse Problem for the Wave Equation with a Polynomial Nonlinearity",
abstract = "For the wave equation containing a nonlinearity in the form of anth order polynomial, we study the problem of determining the coefficients ofthe polynomial depending on the variable. We consider plane waves that propagate in a homogeneous medium in thedirection of a unit vector with a sharp front and incident on an inhomogeneity localized inside acertain ball. It is assumed that the solutions of the problems can be measured at thepoints of the boundary of this ball at the instants of time close to the arrival of the wavefront forall possible values of the vector. It is shown that the solution of the inverse problem is reduced to a series ofX-ray tomography problems.",
author = "Romanov, {V. G.} and Bugueva, {T. V.}",
note = "The work was carried out within the framework of the state assignment for Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, project no. FWNF-2022-0009. Публикация для корректировки.",
year = "2023",
month = mar,
doi = "10.1134/s1990478923010180",
language = "English",
volume = "17",
pages = "163--167",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Inverse Problem for the Wave Equation with a Polynomial Nonlinearity

AU - Romanov, V. G.

AU - Bugueva, T. V.

N1 - The work was carried out within the framework of the state assignment for Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, project no. FWNF-2022-0009. Публикация для корректировки.

PY - 2023/3

Y1 - 2023/3

N2 - For the wave equation containing a nonlinearity in the form of anth order polynomial, we study the problem of determining the coefficients ofthe polynomial depending on the variable. We consider plane waves that propagate in a homogeneous medium in thedirection of a unit vector with a sharp front and incident on an inhomogeneity localized inside acertain ball. It is assumed that the solutions of the problems can be measured at thepoints of the boundary of this ball at the instants of time close to the arrival of the wavefront forall possible values of the vector. It is shown that the solution of the inverse problem is reduced to a series ofX-ray tomography problems.

AB - For the wave equation containing a nonlinearity in the form of anth order polynomial, we study the problem of determining the coefficients ofthe polynomial depending on the variable. We consider plane waves that propagate in a homogeneous medium in thedirection of a unit vector with a sharp front and incident on an inhomogeneity localized inside acertain ball. It is assumed that the solutions of the problems can be measured at thepoints of the boundary of this ball at the instants of time close to the arrival of the wavefront forall possible values of the vector. It is shown that the solution of the inverse problem is reduced to a series ofX-ray tomography problems.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85159896233&origin=inward&txGid=f267428fcaf708740de5fda0dec3585b

UR - https://www.mendeley.com/catalogue/9f828669-5895-3b29-a589-790b41c48e3b/

U2 - 10.1134/s1990478923010180

DO - 10.1134/s1990478923010180

M3 - Article

VL - 17

SP - 163

EP - 167

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -

ID: 59808934