On the existence of global attractors for one class of cascade systems

We investigate the qualitative behavior of solutions of cascade systems without uniqueness. We prove that solutions of a reaction-diffusion system perturbed by a system of ordinary differential equations and solutions of a system of equations of a viscous incompressible liquid with passive components form families of many-valued semiprocesses for which a compact global attractor exists in the phase space.__________Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1287–1291, September, 2004.