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Mat. Zametki, 2012, Volume 92, Issue 2, Pages 225–240 (Mi mz8842)  

This article is cited in 25 scientific papers (total in 25 papers)

Multivalued Dynamics of Solutions of Autonomous Operator Differential Equations with Pseudomonotone Nonlinearity

P. O. Kas'yanov

National Technical University of Ukraine "Kiev Polytechnic Institute"

Abstract: We consider nonlinear autonomous operator differential equations with pseudomonotone dependence between the defining parameters of the problem and study the dynamics of all weak solutions on the positive time semiaxis. We prove the existence of a trajectory and a global attractor and study their structure. As a possible application, we consider the class of high-order nonlinear parabolic equations.

Keywords: nonlinear operator differential equation, pseudomonotone nonlinearity, trajectory attractor, global attractor, dynamic semigroup, high-order nonlinear parabolic equation

DOI: https://doi.org/10.4213/mzm8842

Full text: PDF file (595 kB)
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English version:
Mathematical Notes, 2012, 92:2, 205–218

Bibliographic databases:

UDC: 517.9
Received: 18.06.2010
Revised: 12.07.2011

Citation: P. O. Kas'yanov, “Multivalued Dynamics of Solutions of Autonomous Operator Differential Equations with Pseudomonotone Nonlinearity”, Mat. Zametki, 92:2 (2012), 225–240; Math. Notes, 92:2 (2012), 205–218

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    3. P. O. Kasyanov, L. S. Paliichuk, A. N. Tkachuk, “Metod mnogoznachnykh polugrupp operatorov v issledovanii dolgosrochnykh prognozov upravlyaemykh pezoelektricheskikh polei”, Chebyshevskii sb., 15:2 (2014), 21–32  mathnet
    4. O. V. Kapustyan, P. O. Kasyanov, J. Valero, “Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term”, Discrete Contin. Dyn. Syst., 34:10 (2014), 4155–4182  crossref  mathscinet  zmath  isi
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    6. P. Kalita, G. Łukaszewicz, “Global attractors for multivalued semiflows with weak continuity properties”, Nonlinear Anal., 101 (2014), 124–143  crossref  mathscinet  zmath  isi
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    14. A. A. Ilyin, V. V. Chepyzhov, “On Strong Convergence of Attractors of Navier–Stokes Equations in the Limit of Vanishing Viscosity”, Math. Notes, 101:4 (2017), 746–750  mathnet  crossref  crossref  mathscinet  isi  elib
    15. V. Chepyzhov, A. Ilyin, S. Zelik, “Strong trajectory and global $W^{1,p}$-attractors for the damped-driven Euler system in $\mathbb R^2$”, Discrete Contin. Dyn. Syst. Ser. B, 22:5 (2017), 1835–1855  crossref  mathscinet  zmath  isi  scopus
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    18. Zgurovsky M.Z., Kasyanov P.O., “Method of Artificial Control and the 3D Navier-Stokes System”, Optimization Methods and Applications: in Honor of Ivan V. Sergienko'S 80Th Birthday, Springer Optimization and Its Applications, 130, eds. Butenko S., Pardalos P., Shylo V., Springer International Publishing Ag, 2017, 585–600  crossref  mathscinet  zmath  isi  scopus
    19. M. Z. Zgurovsky, P. O. Kasyanov, “Regularity of solutions for nonlinear systems”: M. Z. Zgurovsky, P. O. Kasyanov, Qualitative and Quantitative Analysis of Nonlinear Systems: Theory and Applications, Studies in Systems Decision and Control, 111, Springer International Publishing Ag, 2018, 47–68  crossref  mathscinet  isi  scopus
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