Boundary value problem for a global-in-time parabolic equation Full article
| Journal |
Mathematical Methods in the Applied Sciences
ISSN: 0170-4214 |
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| Output data | Year: 2021, Volume: 44, Number: 1, Pages: 1118-1126 Pages count : 9 DOI: 10.1002/mma.6816 | ||
| Tags | initial boundary value problem; nonlocal-in-time parabolic equation; solvability; uniqueness | ||
| Authors |
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| Affiliations |
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Funding (1)
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Российский научный фонд Российский научный фонд |
19-11-00069 |
Abstract:
The aim of this paper is to draw attention to an interesting semilinear parabolic equation that arose when describing the chaotic dynamics of a polymermolecule in a liquid. This equation is nonlocal in time and contains a term, called the interaction potential, that depends on the time-integral of the solution over the entire interval of solving the problem. In fact, one needs to know the “future” in order to determine the coefficient in this term, that is, the causality principle is violated. The existence of a weak solution of the initial boundary value problem
is proven. The interaction potential satisfies fairly general conditions and can have arbitrary growth at infinity. The uniqueness of this solution is established with restrictions on the length of the considered time interval.
Cite:
Starovoitov V.N.
Boundary value problem for a global-in-time parabolic equation
Mathematical Methods in the Applied Sciences. 2021. V.44. N1. P.1118-1126. DOI: 10.1002/mma.6816 WOS Scopus РИНЦ OpenAlex
Boundary value problem for a global-in-time parabolic equation
Mathematical Methods in the Applied Sciences. 2021. V.44. N1. P.1118-1126. DOI: 10.1002/mma.6816 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000561116300001 |
| Scopus: | 2-s2.0-85089558764 |
| Elibrary: | 45376102 |
| OpenAlex: | W3080247405 |