Реферат: We study the solvability of boundary value problems nonlocal with respect to the spatial variable with the generalized Samarskii–Ionkin condition for parabolic equations h(t)ut − ∂ ∂x(a(x)ux)+c(x,t)u = f(x,t), 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. Bibliography:21 titles.

Библиографическая ссылка: Kozhanov A.I.
Initial-Boundary Value Problems with Generalized Samarskii–Ionkin Condition for Parabolic Equations with Arbitrary Evolution Direction
Journal of Mathematical Sciences (United States). 2023. V.274. N2. P.228-240. DOI: 10.1007/s10958-023-06591-y Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	30 июн. 2023 г.
Опубликована в печати:	16 авг. 2023 г.
Опубликована online:	16 авг. 2023 г.

Идентификаторы БД:

Scopus:	2-s2.0-85168145489
РИНЦ:	62755299
OpenAlex:	W4385875477

Цитирование в БД:

БД	Цитирований
OpenAlex	3
Scopus	6
РИНЦ	6

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