Abstract:
We consider the solvability of boundary value problems and some inverse problems for operator-differential equations of odd order which can be referred to as mixed type equations since the coefficient of the higher order time derivative can change sign. Studying the general classes of boundary value problems with nonlocal boundary conditions, we establish the existence and uniqueness theorems of regular solutions under some conditions on data.
Keywords:operator-differential equation, nonlocal boundary value problem, inverse problem, mixed type equation.
Citation:
S. G. Pyatkov, “Boundary value and inverse problems for some classes of nonclassical operator-differential equations”, Sibirsk. Mat. Zh., 62:3 (2021), 603–618; Siberian Math. J., 62:3 (2021), 489–502
\Bibitem{Pya21}
\by S.~G.~Pyatkov
\paper Boundary value and inverse problems for some classes of nonclassical operator-differential equations
\jour Sibirsk. Mat. Zh.
\yr 2021
\vol 62
\issue 3
\pages 603--618
\mathnet{http://mi.mathnet.ru/smj7581}
\crossref{https://doi.org/10.33048/smzh.2021.62.312}
\elib{https://elibrary.ru/item.asp?id=46849996}
\transl
\jour Siberian Math. J.
\yr 2021
\vol 62
\issue 3
\pages 489--502
\crossref{https://doi.org/10.1134/S0037446621030125}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85106974724}
Linking options:
https://www.mathnet.ru/eng/smj7581
https://www.mathnet.ru/eng/smj/v62/i3/p603
This publication is cited in the following 4 articles:
N. G. Nikolaeva, O. V. Gavrilova, N. A. Manakova, “Investigation of the uniqueness solution of the Showalter–Sidorov problem for the mathematical Hoff model. Phase space morphology”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 17:1 (2024), 49–63
A. V. Keller, “O napravleniyakh issledovanii uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:4 (2023), 5–32
N. A. Manakova, O. V. Gavrilova, K. V. Perevozchikova, “Polulineinye modeli sobolevskogo tipa. Needinstvennost resheniya zadachi Shouoltera – Sidorova”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:1 (2022), 84–100
M. M. Turov, V. E. Fedorov, B. T. Kien, “Linear inverse problems for multi-term equations with Riemann — Liouville derivatives”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 38 (2021), 36–53