Solvability in Hölder spaces of an inverse problem on chaotic dynamics of a polymer chain

Solvability in Hölder spaces of an inverse problem on chaotic dynamics of a polymer chain Full article

Journal

Quarterly of Applied Mathematics
ISSN: 0033-569X

Output data

Year: 2025, DOI: 10.1090/qam/1703

Tags

Nonlocal in time parabolic equation, inverse problem, solvability, Hölder spaces, polymer chain, chaotic dynamics

Authors

Fomenko A. ¹ , Starovoitov V. ¹

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Lavrentyev prospekt 15, Novosibirsk, 630090, Russia

This paper deals with an inverse problem for a quasi-linear parabolic partial differential equation that contains a nonlocal in time term that includes an integral of the solution over the entire time interval where the problem is considered. Moreover, the overdetermination condition for this inverse problem is nonlocal in space. So, the problem has a double nonlocality: in time and in space. This problem describes the chaotic dynamics of a polymer chain in a liquid. The time variable corresponds to the arc length along the chain. The time nonlocality stands in the argument of the so-called interaction potential. Its appearance is caused by the fact that the motion of each link of a chain is affected by all other links through the surrounded fluid. The solvability of the problem in Hölder spaces in the case of a bounded interaction potential is proven. Moreover, the solvability is also proven in the case of an unbounded potential with certain restrictions on its behavior on some finite interval.

Fomenko A. , Starovoitov V.
Solvability in Hölder spaces of an inverse problem on chaotic dynamics of a polymer chain
Quarterly of Applied Mathematics. 2025. DOI: 10.1090/qam/1703 WOS РИНЦ OpenAlex

Submitted:	Dec 3, 2024
Published online:	Jan 7, 2025

Web of science:	WOS:001392583600001
Elibrary:	80285726
OpenAlex:	W4406140432

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