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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 εF (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 ε > 0 this system has a global attractor.doi:10.3934/dcdsb.2017111 fatcat:37mmqhmo25bhfo2zboqia4u3hq