ω-Limit Sets of Impulsive Semigroups for Hyperbolic Equations
journal contribution
posted on 2023-10-12, 20:51authored byPetro FeketaPetro Feketa, Juliya Fedorenko, Dmytro Bezushchak, Anna Sukretna
In this paper, we investigate the qualitative behavior of an evolutionary problem consisting of a hyperbolic dissipative equation whose trajectories undergo instantaneous impulsive discontinuities at the moments when the energy functional reaches a certain threshold value. The novelty of the current study is that we consider the case in which the entire infinite-dimensional phase vector undergoes an impulsive disturbance. This substantially broadens the existing results, which admit discontinuities for only a finite subset of phase coordinates. Under fairly general conditions on the system parameters, we prove that such a problem generates an impulsive dynamical system in the natural phase space, and its trajectories have nonempty compact ω-limit sets.
History
Preferred citation
Feketa, P., Fedorenko, J., Bezushchak, D. & Sukretna, A. (n.d.). ω-Limit Sets of Impulsive Semigroups for Hyperbolic Equations. Axioms, 12(10), 918-918. https://doi.org/10.3390/axioms12100918