A. I. Kozhanov, A. N. Artyushin, V. V. Shubin, “Boundary problems for parabolic equations with degenerate boundary condition of the third kind”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 503,Pages <nobr>64

MATHEMATICS

Boundary problems for parabolic equations with degenerate boundary condition of the third kind

A. I. Kozhanov^a, A. N. Artyushin^a, V. V. Shubin^b

^a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: 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 $W_2^{2,1}$.

Keywords: second-order parabolic equations, boundary value problems, degenerate boundary condition of the third kind, uniqueness and nonuniqueness of solutions, existence of solutions.

UDC: 517.95

Presented: E. I. Moiseev
Received: 02.12.2021
Revised: 02.12.2021
Accepted: 03.02.2022

DOI: 10.31857/S268695432202014X