Geodesic
Solvability of a boundary value problem of chaotic dynamics of polymer molecule in the case of bounded interaction potential
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1714-1719.

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This paper deals with a boundary value problem for a parabolic differential equation that describes a chaotic motion of a polymer chain in water. The equation is nonlocal in time as well as in space. It includes a so called interaction potential that depends on the integrals of the solution over the entire time interval and over the space domain where the problem is being solved. The time nonlocality appears since the time plays the role of the arc length along the chain and each segment interacts with all others through the surrounding fluid. The weak solvability of the problem is proven for the case of the bounded continuous interaction potential. The proof of the solvability does not use any continuity properties of the solution with respect to the time and is based on the energy estimate only.
Mots-clés : nonlocal parabolic equation
Keywords: initial boundary value problem, solvability. 
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V. N. Starovoitov. Solvability of a boundary value problem of chaotic dynamics of polymer molecule in the case of bounded interaction potential. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1714-1719. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a55/

[1] V.N. Starovoitov, B.N. Starovoitova, “Modeling the dynamics of polymer chains in water solution. Application to sensor design”, J. Phys.: Conf. Ser., 894 (2017), 012088 | DOI

[2] A.Sh. Lyubanova, “On nonlocal problems for systems of parabolic equations”, J. Math. Anal. Appl., 421:2 (2015), 1767–1778 | DOI | MR | Zbl

[3] V.N. Starovoitov, “Initial boundary value problem for a nonlocal in time parabolic equation”, Sib. Èlektron. Mat. Izv., 15 (2018), 1311–1319 | MR | Zbl

[4] V.N. Starovoitov, “Boundary value problem for a global-in-time parabolic equation”, Math. Methods Appl. Sci., 44:1 (2021), 1118–1126 | DOI | MR | Zbl

[5] C. Walker, “Strong solutions to a nonlocal-in-time semilinear heat equation”, Q. Appl. Math., 79:2 (2021), 265–272 | DOI | MR | Zbl

[6] J.D. Djida, G.F.F. Gounoue, Y.K. Tchaptchie, A global in time parabolic equation for symmetric Lévy operators, 2021, arXiv: 2102.07278

[7] V.N. Starovoitov, “Weak solvability of a boundary value problem for a parabolic equation with a global-in-time term that contains a weighted integral”, J. Elliptic Parabol. Equ., 7:2 (2021), 623–634 | DOI | MR | Zbl

[8] L.C. Evans, Partial differential equations, Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, 1998 | MR | Zbl