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Matematicheskie Zametki, 1998, Volume 63, Issue 5, Pages 774–784
DOI: https://doi.org/10.4213/mzm1344 (Mi mzm1344) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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

I. D. Chueshov

V. N. Karazin Kharkiv National University
Full-text PDF (237 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm1344
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.
Received: 05.05.1996
English version:
Mathematical Notes, 1998, Volume 63, Issue 5, Pages 679–687
DOI: https://doi.org/10.1007/BF02312850
Bibliographic databases:
UDC: 517.94
Language: Russian
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
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\yr 1998
\vol 63
\issue 5
\pages 774--784
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\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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000076726600016}
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  • https://www.mathnet.ru/eng/mzm1344
  • https://doi.org/10.4213/mzm1344
  • https://www.mathnet.ru/eng/mzm/v63/i5/p774
    • This publication is cited in the following 6 articles:
    1. Soner Çelen, Kamil Kahveci, Ugur Akyol, “Single Layer Drying Behavior of Apple Slices in a Microwave Dryer”, DDF, 312-315 (2011), 842  crossref
    2. 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
    3. 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
    4. Ch. Bernier-Kazantsev, I.D. Chueshov, “The finiteness of determining degrees of freedom for the quasi-geostrophic multi-layer ocean model”, Nonlinear Analysis: Theory, Methods & Applications, 42:8 (2000), 1499  crossref
    5. Igor D. Chueshov, “On determining functionals for stochastic navier-stokes equations”, Stochastics and Stochastic Reports, 68:1-2 (1999), 45  crossref
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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