Initial-Boundary Value Problems with Generalized Samarskii–Ionkin Condition for Parabolic Equations with Arbitrary Evolution Direction Full article
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Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795 |
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| Output data | Year: 2023, Volume: 274, Number: 2, Pages: 228-240 Pages count : 13 DOI: 10.1007/s10958-023-06591-y | ||||
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0008 |
Abstract:
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.
Cite:
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
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
Dates:
| Submitted: | Jun 30, 2023 |
| Published print: | Aug 16, 2023 |
| Published online: | Aug 16, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85168145489 |
| Elibrary: | 62755299 |
| OpenAlex: | W4385875477 |