Attracting sets for one class of asymptotically compact systems with pulsed perturbation

The authors consider the pulsed dynamical systems generated by evolutionary processes. trajectories of these processes undergo perturbation when energy functional reaches some fixed limit value. generalization classical theory global attractors infinite dimensional in case with impulse actions is carried out. It established that for dissipative system asymptotically compact semigroup, there exists a uniform attractor, i.e., uniformly attracting set, minimal among all such sets phase space system. result applied to weakly nonlinear wave equation dissipation, which are subjected impulsive perturbations upon attainment certain subset space, so called set.