Mykola Perestyuk and Oleksiy Kapustyan

Long-Time Behavior of Evolution Inclusion with Non-Damped Impulsive Effects

abstract:
In this paper we consider an evolution inclusion with impulse effects at fixed moments of time from the point of view of the theory of global attractors. For an upper semicontinuous multivalued term which does not provide the uniqueness of the Cauchy problem, we give sufficient conditions on non-damped multivalued impulse perturbations, which allow us to construct a multivalued non-autonomous dynamical system and prove for it the existence of a compact global attractor in the phase space.

Mathematics Subject Classification: 35B40, 35B41, 35K55, 35K57, 37B25, 58C06

Key words and phrases: Evolution inclusion, impulse perturbation, multivalued dynamical system, global attractor