TY - JOUR

T1 - Existence and Uniqueness of the Solution to a Degenerate Third Boundary Value Problem for a Multidimensional Parabolic Equation

AU - Kozhanov, A. I.

AU - Shubin, V. V.

N1 - Funding Information: The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–281 on April 5, 2022 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/7

Y1 - 2022/7

N2 - We study the well-posedness of a third boundary value problem fora multidimensional parabolic equation in the case when the coefficient of theconormal derivative vanishes at some points.We show that under some conditions on the sign of this coefficientthere exists nonexistence or nonuniqueness of a solution in the conventionalanisotropic Sobolev space.Using the regularization method, we prove existence and uniqueness theoremsfor the regular solution in suitable weighted spaces.

AB - We study the well-posedness of a third boundary value problem fora multidimensional parabolic equation in the case when the coefficient of theconormal derivative vanishes at some points.We show that under some conditions on the sign of this coefficientthere exists nonexistence or nonuniqueness of a solution in the conventionalanisotropic Sobolev space.Using the regularization method, we prove existence and uniqueness theoremsfor the regular solution in suitable weighted spaces.

KW - 517.95

KW - degeneration

KW - existence

KW - parabolic equation

KW - third boundary value problem

KW - uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85135023640&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4e2ad13c-9973-34c8-88be-5ca0136bf348/

U2 - 10.1134/S0037446622040139

DO - 10.1134/S0037446622040139

M3 - Article

AN - SCOPUS:85135023640

VL - 63

SP - 723

EP - 734

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -