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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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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