Control Problems for Equations with a Spectral Parameter and a Discontinuous Operator under Perturbations

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Математика и физика. Mathematics & Physics. 2012 5 (2)
Potapov, Dmitry K.
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control problems; spectral parameter; discontinuous operator; external perturbation; "pertur- bation - control - state"; variational method; Gol'dshtik model

In Banach spaces control problems for systems with a spectral parameter, an external perturbation and a discontinuous operator are considered. The theorem on resolvability for investigated problems is proved. General results are applied to control problems for distributed systems of the elliptic type with a spectral parameter and discontinuous nonlinearity under an external perturbation. Propositions on resolvability for such problems are established. Control problem with a perturbation in the Goldshtik mathematical model for separated flows of incompressible fluid is considered as an application.

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