Existence and Stability of Uniform Attractors for N-Dimensional Impulsive-Perturbed Parabolic System (original) (raw)

The qualitative theory of differential equations with impulsive perturbations is outlined in [1,10,14], and for impulsive dynamical systems in [3,5,9,11,12]. In the case of an infinite dimensional phase space, the qualitative behavior of dissipative systems is studied in the framework of the theory of global attractors [15]. The generalization of the basic concepts and results of the theory of attractors to infinite-dimensional impulsive dynamical systems was carried out in [4, 7, 13]. The main object of research is the minimal compact uniformly attracting set – uniform attractor. The questions of existence, structure and invariance of uniform attractors for different classes of infinitely dimensional impulsive systems are dealt with in [4,6,7]. In [8], authors proposed the conditions for impulsive semiflows, which guarantee the stability of the non-impulsive part of uniform attractors. In the present paper, we refine these conditions and apply them to the study of the stability of ...