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In this work we consider an impulsive multi-valued dynamical system generated by a parabolic inclusion with upper semicontinuous right-hand side $\varepsilon F(y)$ and with impulsive multi-valued perturbations. Moments of impulses are not fixed and defined by moments of intersection of solutions with some subset of the phase space. We prove that for sufficiently small value of the parameter $\varepsilon>0$ this system has a global attractor.

We consider reaction-diffusion systems in a three-dimensional bounded domain under standard dissipativity conditions and quadratic growth conditions. No smoothness or monotonicity conditions are assumed. We prove that every weak solution is regular and use this fact to show that the global attractor of the corresponding multi-valued semiflow is compact in the space $(H_{0}^{1} (Ω))^{N}$.

In this paper we prove the existence of global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of complex fluids. We also show that the attractors tend to the set of all complete bounded trajectories of the original problem when the parameter of the approximations goes to zero.

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