On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types Научная публикация
| Журнал |
Differential Equations
ISSN: 0012-2661 , E-ISSN: 1608-3083 |
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| Вых. Данные | Год: 2023, Том: 59, Номер: 12, Страницы: 1734-1757 Страниц : 24 DOI: 10.1134/s0012266123120133 | ||||||||
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| Организации |
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Информация о финансировании (1)
| 1 | Российский научный фонд | 23-11-00069 |
Реферат:
The paper discusses the features of constructing numerical schemes for solving coefficient inverse problems for nonlinear partial differential equations of the reaction–diffusion–advection type with data of various types. As input data for the inverse problem, we consider (1) data at the final moment of time, (2) data at the spatial boundary of a domain, (3) data at the position of the reaction front. To solve the inverse problem in all formulations, the gradient method of minimizing the target functional is used. In this case, when constructing numerical minimization schemes, both an approach based on discretization of the analytical expression for the gradient of the functional and an approach based on differentiating the discrete approximation of the functional to be minimized are considered. Features of the practical implementation of these approaches are demonstrated by the example of solving the inverse problem of reconstructing the linear gain coefficient in a nonlinear Burgers-type equation.
Библиографическая ссылка:
Lukyanenko D.V.
, Argun R.
, Borzunov A.A.
, Gorbachev A.V.
, Shinkarev V.D.
, Shishlenin M.A.
, Yagola A.G.
On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types
Differential Equations. 2023. V.59. N12. P.1734-1757. DOI: 10.1134/s0012266123120133 WOS Scopus РИНЦ OpenAlex
On the Features of Numerical Solution of Coefficient Inverse Problems for Nonlinear Equations of the Reaction–Diffusion–Advection Type with Data of Various Types
Differential Equations. 2023. V.59. N12. P.1734-1757. DOI: 10.1134/s0012266123120133 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 28 сент. 2023 г. |
| Принята к публикации: | 15 нояб. 2023 г. |
| Опубликована в печати: | 27 дек. 2023 г. |
| Опубликована online: | 26 февр. 2024 г. |
Идентификаторы БД:
| Web of science: | WOS:001172870000009 |
| Scopus: | 2-s2.0-85186451601 |
| РИНЦ: | 65590236 |
| OpenAlex: | W4392175627 |