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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 26–40 (Mi timm1168)  
This article is cited in 17 scientific papers (total in 17 papers)

On a differential game in an abstract parabolic system

L. A. Vlasenkoa, A. G. Rutkasa, A. A. Chikriib

a V. N. Karazin Kharkiv National University
b Glushkov Institute of Cybernetics NAS Ukraine
Full-text PDF (239 kB) Citations (17)
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Abstract: We consider the game problem of approach for a system whose dynamics is described by a differential operator equation in a Hilbert space. The equation is written in an implicit form with generally non-invertible operator multiplying the derivative. It is assumed that the characteristic operator pencil corresponding to the linear part of the equation satisfies a constraint of parabolic type in a right half-plane. Using the method of resolving functionals, we obtain sufficient conditions for the approach of a dynamical vector of the system to a cylindrical terminal set. Applications to systems described by partial differential equations are considered.
Keywords: differential game, parabolic system, ergodic theorem, pseudoresolvent, generator of a semigroup, set-valued mapping, resolving functional, partial differential equation.
Received: 24.01.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 293, Issue 1, Pages 254–269
DOI: https://doi.org/10.1134/S0081543816050229
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: L. A. Vlasenko, A. G. Rutkas, A. A. Chikrii, “On a differential game in an abstract parabolic system”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 26–40; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 254–269
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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