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On a majorant-minorant criterion for the total preservation of global solvability of distributed controlled systems. (English. Russian original) Zbl 1336.93084
Differ. Equ. 52, No. 1, 111-121 (2016); translation from Differ. Uravn. 52, No. 1, 112-122 (2016).
Summary: For distributed controlled systems that can be represented by a functional-operator equation of the Hammerstein type with an additional term on the right-hand side in the form of a linear operator (an extended equation of the Hammerstein type), we prove a criterion for the total (over the entire set of admissible controls) preservation of global solvability. In this connection, we develop an earlier-proved majorant-minorant criterion for the total preservation of global solvability. As an example, we study a controlled semilinear integro-differential equation describing radiation transport with Compton scattering diagram. The choice of this example is explained, in particular, by the fact that the preceding version of the majorant-minorant criterion is not applicable to it.

MSC:
93C25 Control/observation systems in abstract spaces
93B28 Operator-theoretic methods
93C05 Linear systems in control theory
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