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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 189, Pages 3–130
DOI: https://doi.org/10.36535/0233-6723-2021-189-3-130 (Mi into745) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Attractors, shadowing, and approximation of abstract semilinear differential equations

S. I. Piskarevabc, A. V. Ovchinnikovdc

a Lomonosov Moscow State University, Research Computing Center
b Mari State University, Ioshkar-Ola
c All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
d Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2021-189-3-130
Abstract: The review covers such sections of the theory of approximation of abstract differential equations as the approximation of attractors in the case of hyperbolic stationary points, the shadowing and, finally, the approximation of fractional in time semilinear problems.
Keywords: abstract parabolic equations, general approximation scheme, compact convergence of resolvents, attractor, unstable manifold, stable manifold, upper and lower semicontinuity of attractors, affinity principle, principle of compact approximation, semilinear differential equation, Banach space, periodic solution, Lyapunov stability, hyperbolic equilibrium, semiflow, rotation of a vector field, index of a solution, shadowing, analytic C0-semigroup, semidiscretization, discretization in space, discretization in time, fractional equation, fractional power of an operator, condensing operator.
Funding agency Grant number
Russian Foundation for Basic Research 20-11-50004
21-51-46001
Russian Science Foundation 20-11-20085
This work was supported by the Russian Foundation for Basic Research (project Nos. 20-11-50004 and 21-51-46001) and the Russian Science Foundation (project No. 20-11-20085, for Sec. 5).
Document Type: Article
UDC: 517.988.8
MSC: 34D09, 34G20, 35B41, 35K55, 35K58, 35K90, 35R11, 47J35, 65J08
Language: Russian
Citation: S. I. Piskarev, A. V. Ovchinnikov, “Attractors, shadowing, and approximation of abstract semilinear differential equations”, Functional Analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 189, VINITI, Moscow, 2021, 3–130
Citation in format AMSBIB
\Bibitem{PisOvc21}
\by S.~I.~Piskarev, A.~V.~Ovchinnikov
\paper Attractors, shadowing, and approximation of abstract semilinear differential equations
\inbook Functional Analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 189
\pages 3--130
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into745}
\crossref{https://doi.org/10.36535/0233-6723-2021-189-3-130}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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