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ω-Limit Sets of Impulsive Semigroups for Hyperbolic Equations

journal contribution
posted on 2023-10-12, 20:51 authored by Petro 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

Journal title

Axioms

Volume

12

Issue

10

Pagination

918-918

Publisher

MDPI AG

Publication status

Published online

Online publication date

2023-09-27

ISSN

2075-1680

eISSN

2075-1680

Language

en

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