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The Total Preservation of Unique Global Solvability of the First Kind Operator Equation With Additional Controlled Nonlinearity

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Abstract

For the Cauchy problem associated with an evolutionary operator equation of the first kind with an additional controlled term which nonlinearly depends on the phase variable, in a Banach space, we establish conditions for the total (on the set of admissible controls) preservation of unique global solvability under variation of the control parameter. We also establish the uniform bound for solutions. As examples, we consider initial-boundary value problems that are associated with a pseudoparabolic equation and a system of Oskolkov equations.

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Authors and Affiliations

  1. Nizhni Novgorod State University named after N. I. Lobachevskii, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

    A. V. Chernov

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  1. A. V. Chernov
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Correspondence to A. V. Chernov.

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Original Russian Text © A.V. Chernov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 11, pp. 60–74.

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Chernov, A.V. The Total Preservation of Unique Global Solvability of the First Kind Operator Equation With Additional Controlled Nonlinearity. Russ Math. 62, 53–66 (2018). https://doi.org/10.3103/S1066369X18110063

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  • DOI: https://doi.org/10.3103/S1066369X18110063

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