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

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. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 774–784, May, 1998.