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A remark on sets of determining elements for reaction-diffusion systems. (English. Russian original) Zbl 0918.35069
Math. Notes 63, No. 5, 679-687 (1998); translation from Mat. Zametki 63, No. 5, 774-784 (1998).
Summary: 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.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
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