TY - JOUR

T1 - Boundary Problems for Parabolic Equations with Degenerate Boundary Condition of the Third Kind

AU - Kozhanov, A. I.

AU - Artyushin, A. N.

AU - Shubin, V. V.

N1 - Funding Information: This work was supported by the Mathematical Center in Akademgorodok, agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/4

Y1 - 2022/4

N2 - The solvability of initial-boundary value problems for linear parabolic equations of the second order with a degenerate boundary value condition of the third kind is studied. Sufficient conditions for the existence and uniqueness of solutions are given. It is shown that the degeneration effect can lead to nonuniqueness of solutions in the space (Formula presented.).

AB - The solvability of initial-boundary value problems for linear parabolic equations of the second order with a degenerate boundary value condition of the third kind is studied. Sufficient conditions for the existence and uniqueness of solutions are given. It is shown that the degeneration effect can lead to nonuniqueness of solutions in the space (Formula presented.).

KW - boundary value problems

KW - degenerate boundary condition of the third kind

KW - existence of solutions

KW - second-order parabolic equations

KW - uniqueness and nonuniqueness of solutions

UR - http://www.scopus.com/inward/record.url?scp=85133585275&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=49152565

UR - https://www.mendeley.com/catalogue/a7ed6e7d-04d8-33a6-b6b0-ca7c25e427b6/

U2 - 10.1134/S1064562422020144

DO - 10.1134/S1064562422020144

M3 - Article

AN - SCOPUS:85133585275

VL - 105

SP - 106

EP - 108

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

M1 - 8

ER -