Geodesic
On convexity local conditions for attainable tubes of controlled distributed systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 72-86.

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For a nonlinear functional operator equation being a form of describing for a wide class of controlled initial boundary-value problems, we introduce the concept of abstract attainable set as an analog of the attainable tube concept. We obtain local sufficient conditions for the convexity of such a set. Using the general results is illustrated by example of the mixed boundary-value problem associated with a semilinear hyperbolic equation of the second order and a rather general form.
Keywords: attainable tube, convexity local conditions, functional operator equation, nonlinear distributed systems. 
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A. V. Chernov. On convexity local conditions for attainable tubes of controlled distributed systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 72-86. http://geodesic.mathdoc.fr/item/IVM_2014_11_a7/

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