Geodesic
On the total preservation of univalent global solvability for a first kind operator equation with controlled added nonlinearity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2018), pp. 60-74

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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, system of Oskolkov equations.
Mots-clés : pseudoparabolic equation 
@article{IVM_2018_11_a5,
     author = {A. V. Chernov},
     title = {On the total preservation of univalent global solvability for a first kind operator equation with controlled added nonlinearity},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--74},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_11_a5/}
}
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A. V. Chernov. On the total preservation of univalent global solvability for a first kind operator equation with controlled added nonlinearity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2018), pp. 60-74. http://geodesic.mathdoc.fr/item/IVM_2018_11_a5/