Special Structure of the Solution to the Cauchy Problem for a Parabolic Equation and Inverse Problems | Sciact - Система учета научной деятельности ИМ СО РАН

Special Structure of the Solution to the Cauchy Problem for a Parabolic Equation and Inverse Problems Научная публикация

Журнал

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Вых. Данные

Год: 2026, Том: 67, Номер: 2, Страницы: 350-356 Страниц : 7 DOI: 10.1134/s0037446626020084

Ключевые слова

parabolic equation, cauchy problem, structure of the solution, tomography, inverse problem, uniqueness

Авторы

Romanov V.G. ¹

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, Russia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0029

For an equation of parabolic type whose principal part is the heat operator, we study the Cauchy problem with a point source. A special structure of the solution to this problem is written out. It is based on a representation of the solution as the product of the fundamental solution to the heat equation and a polynomial in powers of t with coefficients depending on the spatial variables. Formulas for computing these coefficients are derived, and an estimate of the remainder term is given. Next, two inverse problems for the original equation are posed. They are then studied on the basis of the obtained structure of the solution to the Cauchy problem. A uniqueness theorem is formulated for the considered inverse problems.

Romanov V.G.
Special Structure of the Solution to the Cauchy Problem for a Parabolic Equation and Inverse Problems
Siberian Mathematical Journal. 2026. V.67. N2. P.350-356. DOI: 10.1134/s0037446626020084 РИНЦ OpenAlex

Поступила в редакцию:	31 дек. 2025 г.
Принята к публикации:	26 янв. 2026 г.
Опубликована online:	28 мар. 2026 г.

≡ РИНЦ:	89161335
≡ OpenAlex:	W7141916289