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The Inverse Problem for a Quasilinear Wave Equation with Memory Научная публикация

Журнал

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Вых. Данные

Год: 2025, Том: 19, Номер: 1, Страницы: 104-130 Страниц : 27 DOI: 10.1134/S1990478925010107

Ключевые слова

nonlinearwave equation, integro-differential equation, equation with memory, forward problem, inverse problem, existence of solution

Авторы

Romanov V.G. ¹ , Bugueva T.V. ^1,2

Организации

1	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2	Novosibirsk State University, Novosibirsk, 630090, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0009

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.

Romanov V.G. , Bugueva T.V.
The Inverse Problem for a Quasilinear Wave Equation with Memory
Journal of Applied and Industrial Mathematics. 2025. V.19. N1. P.104-130. DOI: 10.1134/S1990478925010107 Scopus РИНЦ

Романов В.Г. , Бугуева Т.В.
Обратная задача для квазилинейного волнового уравнения с памятью
Сибирский журнал индустриальной математики. 2025. Т.28. №1. С.38-66. DOI: 10.33048/SIBJIM.2025.28.104 РИНЦ

Поступила в редакцию:	22 нояб. 2024 г.
Принята к публикации:	10 мар. 2025 г.
Опубликована в печати:	2 нояб. 2025 г.
Опубликована online:	2 нояб. 2025 г.

Scopus:	2-s2.0-105020677592
РИНЦ:	83155455

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