Притягувальні множини для одного класу асимптотично компактних систем з імпульсним збуренням

• Main Authors: Kapustyan, Oleksiy, Gorban, Nataliia
• Format: Article
• Language: Ukrainian
• Published: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2021
• Subjects: динамическая система; аттрактор; импульсное возмущение; волновое уравнение; dynamical system; attractor; impulse perturbation; wave equation; динамічна система; атрактор; імпульсне збурення; хвильове рівняння
• Online Access: http://journal.iasa.kpi.ua/article/view/231825

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