Abstract:
For a Cauchy problem associated with an evolutionary operator equation of first kind with controlled additional term depending nonlinearly on a phase variable in a Banach space we obtain sufficient conditions of the total (with respect to a whole set of admissible controls) preservation of univalent global solvability, and also uniform estimate for solutions. As examples we consider initial boundary value problems associated with a pseudoparabolic equation and a system of Oskolkov equations.
Keywords:
evolutionary operator equation of first kind in a Banach space, controlled nonlinearity, total preservation of global solvability, pseudoparabolic equation, system of Oskolkov equations.
Citation:
A. V. Chernov, “On the total preservation of univalent global solvability for a first kind operator equation with controlled added nonlinearity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 11, 60–74; Russian Math. (Iz. VUZ), 62:11 (2018), 53–66
\Bibitem{Che18}
\by A.~V.~Chernov
\paper On the total preservation of univalent global solvability for a first kind operator equation with controlled added nonlinearity
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 11
\pages 60--74
\mathnet{http://mi.mathnet.ru/ivm9413}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 11
\pages 53--66
\crossref{https://doi.org/10.3103/S1066369X18110063}
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https://www.mathnet.ru/eng/ivm9413
https://www.mathnet.ru/eng/ivm/y2018/i11/p60
This publication is cited in the following 7 articles:
A. V. Chernov, “On the Exact Global Controllability
of a Semilinear Evolution Equation”, Diff Equat, 60:3 (2024), 374
A. V. Chernov, “ON EXACT GLOBAL CONTROLLABILITY OF A SEMILINEAR EVOLUTIONARY EQUATION”, Differencialʹnye uravneniâ, 60:3 (2024), 399
A. V. Chernov, “On the existence of optimal control in the problem of optimizing the lowest coefficient of a semilinear evolutionary equation”, Comput. Math. Math. Phys., 63:7 (2023), 1176–1190
A. V. Chernov, “Operator Equations of the Second Kind: Theorems on the Existence and Uniqueness of the Solution and on the Preservation of Solvability”, Diff Equat, 58:5 (2022), 649
A. V. Chernov, “O sokhranenii globalnoi razreshimosti operatornogo uravneniya pervogo roda s upravlyaemoi dobavochnoi nelineinostyu”, Materialy Voronezhskoi vesennei matematicheskoi shkoly
«Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 192, VINITI RAN, M., 2021, 131–141
A. V. Chernov, “On preservation of global solvability of controlled second kind operator equation”, Ufa Math. J., 12:1 (2020), 56–81
Citation in format AMSBIB
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