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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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http://mi.mathnet.ru/eng/mz1344https://doi.org/10.4213/mzm1344 http://mi.mathnet.ru/eng/mz/v63/i5/p774
Citing articles on Google Scholar:
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Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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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
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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
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T. Yu. Semenova, “Conditions on Determining Functionals for Subsets of Sobolev Space”, Math. Notes, 86:6 (2009), 831–841
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