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Russian Mathematics

, Volume 62, Issue 11, pp 53–66 | Cite as

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

  • A. V. ChernovEmail author
Article

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.

Keywords

evolutionary operator equation of the first kind in a Banach space controlled nonlinearity total preservation of unique global solvability pseudoparabolic equation system of Oskolkov equations 

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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Nizhni Novgorod State University named after N. I. LobachevskiiNizhni NovgorodRussia

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