Реферат: In this paper, a coefficient inverse problem for a non-local in time parabolic equation is considered. This equation arose when describing the chaotic motion of a polymer chain in a liquid. The role of time in it is played by the arc length parameter along the chain. The solution is the probability density function that a chain link is located at a particular point in space. Accordingly, the overdetermination condition for the inverse problem is that the integral over space of the solution is equal to one at every moment of time. The position of each chain link is affected by all other links, so the interaction potential included in the equation depends on the integral of the solution to the problem over the entire length of the chain. This means that the parabolic equation under consideration is essentially non-local in time and includes an integral of the solution over the entire time interval over which the problem is being solved. Therefore, to determine some of the coefficients in the equation, it is necessary to know the “future”. This situation is unusual for parabolic equations. The solvability of the problem with homogeneous Neumann boundary conditions is proven without restrictions on the input data size, in particular, on the length of the time interval over which the problem is being solved. It is only assumed that the interaction potential is a bounded function.

Библиографическая ссылка: Abdukarimov F.A. , Starovoitov V.N. , Titova A.A.
Weak solvability of an essentially non-local in time parabolic inverse problem with Neumann boundary conditions
Nonlinear Analysis: Real World Applications. 2026. V.93. 104680 :1-10. DOI: 10.1016/j.nonrwa.2026.104680 WOS Scopus OpenAlex

Даты:

Поступила в редакцию:	19 янв. 2026 г.
Принята к публикации:	2 июн. 2026 г.
Опубликована в печати:	8 июн. 2026 г.
Опубликована online:	8 июн. 2026 г.

Идентификаторы БД:

≡ Web of science:	WOS:001794917900001
≡ Scopus:	2-s2.0-105041228234
≡ OpenAlex:	W7163954366

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