On the total preservation of univalent global solvability for a first kind operator equation with controlled added nonlinearity

A. V. Chernov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2018), pp. 60-74.

Résumé

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.

Détail

Keywords: evolutionary operator equation of first kind in a Banach space, controlled nonlinearity, total preservation of global solvability, system of Oskolkov equations.
Mots-clés : pseudoparabolic equation

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