Geodesic
Control problems for equations with a~spectral parameter and a~discontinuous operator under perturbations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 239-245

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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 Gol'dshtik mathematical model for separated flows of incompressible fluid is considered as an application.
Keywords: control problems, spectral parameter, discontinuous operator, variational method, Gol'dshtik model.
Mots-clés : external perturbation, “perturbation–control–state” 
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     author = {Dmitry K. Potapov},
     title = {Control problems for equations with a~spectral parameter and a~discontinuous operator under perturbations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {239--245},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a9/}
}
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Dmitry K. Potapov. Control problems for equations with a~spectral parameter and a~discontinuous operator under perturbations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 2, pp. 239-245. http://geodesic.mathdoc.fr/item/JSFU_2012_5_2_a9/