Inverse problem for a nonlinear wave equation | Sciact - Система учета научной деятельности ИМ СО РАН

Inverse problem for a nonlinear wave equation Научная публикация

Журнал

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

Вых. Данные

Год: 2022, Том: 16, Номер: 2, Страницы: 333–348 Страниц : DOI: 10.1134/S1990478922020132

Ключевые слова

nonlinear wave equation, inverse problem, integral geometry

Авторы

Romanov V.G. ¹ , Bugueva T.V. ^1,2

Организации

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

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0009

We consider the inverse problem of determining the coefficient of the nonlinear term in an equation whose main part is the wave operator. The properties of the solution of the direct problem are studied; in particular, the existence and uniqueness of a bounded solution in a neighborhood of the characteristic cone is established, and the structure of this solution is written out. The problem of finding the unknown function is reduced to the problem of integral geometry on a family of straight lines with a weight function invariant with respect to rotations around some fixed point. The uniqueness of the solution of the inverse problem is established, and an algorithm for reconstructing the desired function is proposed.

Romanov V.G. , Bugueva T.V.
Inverse problem for a nonlinear wave equation
Journal of Applied and Industrial Mathematics. 2022. V.16. N2. P.333–348. DOI: 10.1134/S1990478922020132 Scopus РИНЦ OpenAlex

Романов В.Г. , Бугуева Т.В.
Обратная задача для нелинейного волнового уравнения
Сибирский журнал индустриальной математики. 2022. Т.25. №2. С.83-100. DOI: 10.33048/SIBJIM.2022.25.206 РИНЦ

Поступила в редакцию:	16 дек. 2021 г.
Принята к публикации:	13 янв. 2022 г.

Scopus:	2-s2.0-85141917191
РИНЦ:	51788432
OpenAlex:	W4312518602

БД	Цитирований
Scopus	8
OpenAlex	7
РИНЦ	5