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The Inverse Problem for a Quasilinear Wave Equation with Memory. / Романов, Владимир Гаврилович; Бугуева, Татьяна Владимировна.

в: Journal of Applied and Industrial Mathematics, Том 19, № 1, 10, 2025, стр. 104-130.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Романов, ВГ & Бугуева, ТВ 2025, 'The Inverse Problem for a Quasilinear Wave Equation with Memory', Journal of Applied and Industrial Mathematics, Том. 19, № 1, 10, стр. 104-130. https://doi.org/10.1134/S1990478925010107

APA

Романов, В. Г., & Бугуева, Т. В. (2025). The Inverse Problem for a Quasilinear Wave Equation with Memory. Journal of Applied and Industrial Mathematics, 19(1), 104-130. [10]. https://doi.org/10.1134/S1990478925010107

Vancouver

Романов ВГ, Бугуева ТВ. The Inverse Problem for a Quasilinear Wave Equation with Memory. Journal of Applied and Industrial Mathematics. 2025;19(1):104-130. 10. doi: 10.1134/S1990478925010107

Author

Романов, Владимир Гаврилович ; Бугуева, Татьяна Владимировна. / The Inverse Problem for a Quasilinear Wave Equation with Memory. в: Journal of Applied and Industrial Mathematics. 2025 ; Том 19, № 1. стр. 104-130.

BibTeX

@article{6599d227e14f4a928825376e83abdbfa,
title = "The Inverse Problem for a Quasilinear Wave Equation with Memory",
abstract = "The forward and inverse problems are investigated for the quasilinear wave equation □u−q(x)u2−K∗u=0 where the kernel K(x,t) is represented in the form K(x,t)=p(x)K0(t) with p(x) being a continuous function. The inverse problem is devoted to the determination of the compact functions q(x) and p(x). Traces of the derivative with respect to x of two solutions to the forward initial–boundary value problem related to two arbitrary boundary data are given for x=0 on the finite segment [0,T] as an additional information for the solution to the inverse problem. The conditions for the unique solvability of the forward problem are found. A local existence and uniqueness theorem is proved for the inverse problem.",
keywords = "NONLINEARWAVE EQUATION, INTEGRO-DIFFERENTIAL EQUATION, EQUATION WITH MEMORY, FORWARD PROBLEM, INVERSE PROBLEM, EXISTENCE OF SOLUTION",
author = "Романов, {Владимир Гаврилович} and Бугуева, {Татьяна Владимировна}",
note = "Romanov V.G., Bugueva T.V. The Inverse Problem for a Quasilinear Wave Equation with Memory // Journal of Applied and Industrial Mathematics. – 2025. – Vol. 19. - No. 1. – P. 104-130. – DOI 10.1134/S1990478925010107. – EDN QRKZEE. This work was carried out within the framework of the state assignment of the Sobolev Institute of Mathematics SB RAS, project no. FWNF-2022-0009.",
year = "2025",
doi = "10.1134/S1990478925010107",
language = "English",
volume = "19",
pages = "104--130",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - The Inverse Problem for a Quasilinear Wave Equation with Memory

AU - Романов, Владимир Гаврилович

AU - Бугуева, Татьяна Владимировна

N1 - Romanov V.G., Bugueva T.V. The Inverse Problem for a Quasilinear Wave Equation with Memory // Journal of Applied and Industrial Mathematics. – 2025. – Vol. 19. - No. 1. – P. 104-130. – DOI 10.1134/S1990478925010107. – EDN QRKZEE. This work was carried out within the framework of the state assignment of the Sobolev Institute of Mathematics SB RAS, project no. FWNF-2022-0009.

PY - 2025

Y1 - 2025

N2 - The forward and inverse problems are investigated for the quasilinear wave equation □u−q(x)u2−K∗u=0 where the kernel K(x,t) is represented in the form K(x,t)=p(x)K0(t) with p(x) being a continuous function. The inverse problem is devoted to the determination of the compact functions q(x) and p(x). Traces of the derivative with respect to x of two solutions to the forward initial–boundary value problem related to two arbitrary boundary data are given for x=0 on the finite segment [0,T] as an additional information for the solution to the inverse problem. The conditions for the unique solvability of the forward problem are found. A local existence and uniqueness theorem is proved for the inverse problem.

AB - The forward and inverse problems are investigated for the quasilinear wave equation □u−q(x)u2−K∗u=0 where the kernel K(x,t) is represented in the form K(x,t)=p(x)K0(t) with p(x) being a continuous function. The inverse problem is devoted to the determination of the compact functions q(x) and p(x). Traces of the derivative with respect to x of two solutions to the forward initial–boundary value problem related to two arbitrary boundary data are given for x=0 on the finite segment [0,T] as an additional information for the solution to the inverse problem. The conditions for the unique solvability of the forward problem are found. A local existence and uniqueness theorem is proved for the inverse problem.

KW - NONLINEARWAVE EQUATION

KW - INTEGRO-DIFFERENTIAL EQUATION

KW - EQUATION WITH MEMORY

KW - FORWARD PROBLEM

KW - INVERSE PROBLEM

KW - EXISTENCE OF SOLUTION

UR - https://www.scopus.com/pages/publications/105020677592

UR - https://www.elibrary.ru/item.asp?id=83155455

UR - https://www.elibrary.ru/item.asp?id=82971303

U2 - 10.1134/S1990478925010107

DO - 10.1134/S1990478925010107

M3 - Article

VL - 19

SP - 104

EP - 130

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

M1 - 10

ER -

ID: 72127476