An inverse problem for the semilinear wave equation with a nonlinear integral operator Научная публикация
| Журнал |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Вых. Данные | Год: 2025, Том: 66, Номер: 2, Страницы: 326-344 Страниц : 19 DOI: 10.1134/S0037446625020107 | ||
| Ключевые слова | semilinear wave equation with memory, inverse problem, structure of solutions, integral geometry, uniqueness, solution method | ||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0009 |
Реферат:
We consider an integrodifferential equation whose leading part coincides with the wave operator, while the lower part includes the nonlinear term q(x)um with m>1 and a nonlinear integral operator. This operator models the memory of a medium and includes a variable coefficient p(x). For the original equation we study the structure of the solution to the Cauchy problem with zero initial data and a pulsating source localized at some point (y,0) of the four-dimensional space of variables (x,t). We assume that q(x) and p(x) are compactly supported functions with supports lying in the ball B0 centered at the origin and bounded by some sphere S0, while the point y lies on a sphere S concentric with S0 but of larger radius. The point y is a parameter of the problem and can run over the whole sphere S. We study the inverse problem of determining the functions q(x) and p(x) on B0. For that we use the following information. For every point y on the sphere S and a point x on a certain part of the same sphere we define the solution to the Cauchy problem for the original integrodifferential equation for the moments of time close to the arrival of the wave from the source at y to x. We show that this inverse problem reduces to two identical integral geometry problems on the family of straight lines with a prescribed weight function invariant under all rotations about the center of the ball B0. We establish a uniqueness theorem and propose a method for solving these problems.
Библиографическая ссылка:
Romanov V.G.
An inverse problem for the semilinear wave equation with a nonlinear integral operator
Siberian Mathematical Journal. 2025. V.66. N2. P.326-344. DOI: 10.1134/S0037446625020107 Scopus РИНЦ OpenAlex
An inverse problem for the semilinear wave equation with a nonlinear integral operator
Siberian Mathematical Journal. 2025. V.66. N2. P.326-344. DOI: 10.1134/S0037446625020107 Scopus РИНЦ OpenAlex
Оригинальная:
Романов В.Г.
Обратная задача для полулинейного волнового уравнения с нелинейным интегральным оператором
Сибирский математический журнал. 2025. Т.66. №2. С.245-265. DOI: 10.33048/smzh.2025.66.210 РИНЦ
Обратная задача для полулинейного волнового уравнения с нелинейным интегральным оператором
Сибирский математический журнал. 2025. Т.66. №2. С.245-265. DOI: 10.33048/smzh.2025.66.210 РИНЦ
Даты:
| Поступила в редакцию: | 16 янв. 2025 г. |
| Принята к публикации: | 25 февр. 2025 г. |
| Опубликована в печати: | 23 апр. 2025 г. |
| Опубликована online: | 23 апр. 2025 г. |
Идентификаторы БД:
| Scopus: | 2-s2.0-105000516866 |
| РИНЦ: | 80504520 |
| OpenAlex: | W4408735203 |
Цитирование в БД:
Пока нет цитирований