TY - JOUR

T1 - Initial-Boundary Value Problems with Generalized Samarskii–Ionkin Condition for Parabolic Equations with Arbitrary Evolution Direction

AU - Kozhanov, Alexandr

N1 - The work was carried out within the framework of the state task of Sobolev Institute of Mathematics (project FWNF -2022 -0008). Публикация для корректировки.

PY - 2023/8

Y1 - 2023/8

N2 - We study the solvability of boundary value problems nonlocal with respect to the spatial variable with the generalized Samarskii–Ionkin condition for parabolic equations (Formula Presented.) where x ∈ (0, 1), t ∈ (0, T) and h(t), a(x), c(x, t), f(x, t) are given functions. If a(x) is positive, then the function h(t) can have different signs at different points of [0, T] or even vanish on a set of positive measure in [0, T]. We prove the existence and uniqueness of regular solutions, i.e., solutions possessing all weak derivatives (in the sense of Sobolev) occurring in the corresponding equation. The obtained results are new even for the classical Samarskii–Ionkin problem for the heat equation.

AB - We study the solvability of boundary value problems nonlocal with respect to the spatial variable with the generalized Samarskii–Ionkin condition for parabolic equations (Formula Presented.) where x ∈ (0, 1), t ∈ (0, T) and h(t), a(x), c(x, t), f(x, t) are given functions. If a(x) is positive, then the function h(t) can have different signs at different points of [0, T] or even vanish on a set of positive measure in [0, T]. We prove the existence and uniqueness of regular solutions, i.e., solutions possessing all weak derivatives (in the sense of Sobolev) occurring in the corresponding equation. The obtained results are new even for the classical Samarskii–Ionkin problem for the heat equation.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85168145489&origin=inward&txGid=4149797a7e3affe6630b79dc9bd3ccfb

UR - https://www.mendeley.com/catalogue/fa890204-fd8d-3128-ad84-5ac67ddf8e55/

U2 - 10.1007/s10958-023-06591-y

DO - 10.1007/s10958-023-06591-y

M3 - Article

VL - 274

SP - 228

EP - 240

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 2

ER -