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Mat. Zametki, 1998, Volume 63, Issue 5, Pages 774–784 (Mi mz1344)  

This article is cited in 3 scientific papers (total in 3 papers)

A remark on sets of determining elements for reaction-diffusion systems

I. D. Chueshov

V. N. Karazin Kharkiv National University

Abstract: For a class of systems of parabolic equations, conditions represented by a finite set of linear functionals on the phase space that uniquely determine the long-time behavior of solutions are found. The cases in which it is sufficient to define these determining functionals only on a part of the components of the state vector are singled out. As examples, systems describing the Belousov–Zhabotinsky reaction and the two-dimensional Navier–Stokes equations are considered.

DOI: https://doi.org/10.4213/mzm1344

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English version:
Mathematical Notes, 1998, 63:5, 679–687

Bibliographic databases:

UDC: 517.94
Received: 05.05.1996

Citation: I. D. Chueshov, “A remark on sets of determining elements for reaction-diffusion systems”, Mat. Zametki, 63:5 (1998), 774–784; Math. Notes, 63:5 (1998), 679–687

Citation in format AMSBIB
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\by I.~D.~Chueshov
\paper A remark on sets of determining elements for reaction-diffusion systems
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 5
\pages 774--784
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1683651}
\zmath{https://zbmath.org/?q=an:0918.35069}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 5
\pages 679--687
\crossref{https://doi.org/10.1007/BF02312850}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000076726600016}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. D. Chueshov, “Theory of functionals that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems”, Russian Math. Surveys, 53:4 (1998), 731–776  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. T. Yu. Semenova, “Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of differential equations of the form $u-F(x,u,u')$”, Izv. Math., 71:1 (2007), 149–180  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. T. Yu. Semenova, “Conditions on Determining Functionals for Subsets of Sobolev Space”, Math. Notes, 86:6 (2009), 831–841  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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