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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 5, Pages 36–50 (Mi ivm8796)  

Uniformly continuous dependence of a solution to a controlled functional operator equation on a shift of control

A. V. Chernov

Chair of Mathematical Physics, Nizhny Novgorod State University, Nizhny Novgorod, Russia

Abstract: We establish sufficient conditions for the uniformly (with respect to the set of admissible controls) continuous dependence of a solution to a controlled functional operator equation on a shift of control along a vector of independent variables. The shift of control may mean, in particular, some time delay (or outstripping) of the control. We illustrate the use of general results by an example of a mixed boundary value problem associated with a wave equation.

Keywords: nonlinear functional operator equation, Lebesgue spaces, continuous dependence of solution, shift of control, delay of control.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:5, 29–41
UDC: 517.957+517.988+517.977
Received: 05.03.2012

Citation: A. V. Chernov, “Uniformly continuous dependence of a solution to a controlled functional operator equation on a shift of control”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 5, 36–50; Russian Math. (Iz. VUZ), 57:5 (2013), 29–41

Citation in format AMSBIB
\Bibitem{Che13}
\by A.~V.~Chernov
\paper Uniformly continuous dependence of a~solution to a~controlled functional operator equation on a~shift of control
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 5
\pages 36--50
\mathnet{http://mi.mathnet.ru/ivm8796}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 5
\pages 29--41


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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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