Abstract:
Research of stationary Sobolev type equations were the basis for the study of a variety of different problems, such as optimal control problem, Leontief type system, the optimal measurement problems, etc. Nonstationary Sobolev type equations have been studied only in fragments. In this article the methods required to find solutions to such equations are substantiated. Namely, we investigate degenerate flows of solving operators with which shows the solvability of initial value problems for nonstationary equations of Sobolev type.
Keywords:
relatively bounded operator, degenerate groups of operators, Cauchy problem, Showalter–Sidorov problem.
Received: 20.05.2016
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: Russian
Citation:
M. A. Sagadeeva, “Degenerate flows of solving operators for nonstationary Sobolev type equations”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 9:1 (2017), 22–30
This publication is cited in the following 7 articles:
M. A. Sagadeeva, S. A. Zagrebina, “Ustoichivost statsionarnogo resheniya neavtonomnoi linearizovannoi modeli Khoffa na geometricheskom grafe”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 17:2 (2024), 40–50
A. V. Buevich, M. A. Sagadeeva, S. A. Zagrebina, “Stability of a stationary solution to one class of non-autonomous Sobolev type equations”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:3 (2023), 65–73
A. V. Keller, “Sobolev-type systems and applied problems”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:4 (2023), 5–32
S. A. Zagrebina, A. S. Konkina, “The non-classical models of mathematical physics the multipoint initial-final value condition”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 15:1 (2022), 60–83
A. V. Keller, “K 30-letiyu seminara po uravneniyam sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:1 (2021), 126–130
Alevtina V. Keller, Minzilia A. Sagadeeva, Springer Proceedings in Mathematics & Statistics, 325, Semigroups of Operators – Theory and Applications, 2020, 263
M. A. Sagadeeva, A. A. Stenina, “Reshenie nachalno-konechnoi zadachi dlya nestatsionarnoi sistemy leontevskogo tipa”, J. Comp. Eng. Math., 6:2 (2019), 42–53
Citation in format AMSBIB
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