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Uniform attractor of impulse-perturbed reaction-diffusion system

Oleksiy Kapustyan, Olena Kapustian, Ihor Korol and Bruno Rubino

Vol. 11 (2023), No. 1, 45–55
DOI: 10.2140/memocs.2023.11.45
Abstract

The paper deals with the existence and invariance of uniform attractors of impulse-perturbed reaction-diffusion system. Moments of impulsive perturbation are not fixed and are determined by the getting of trajectory into a given subset M of the phase space. At the moment of getting, the phase variable undergoes a fixed increment. It is proved that such a problem generates impulsive dynamical system that has the uniform attractor Θ, and the set Θ M is invariant with respect to the impulsive semiflow.

Keywords
impulsive dynamical system, reaction-diffusion system, attractor
Mathematical Subject Classification
Primary: 35B41, 35K05, 35Q79, 35R12
Milestones
Received: 11 August 2022
Revised: 18 November 2022
Accepted: 10 January 2023
Published: 23 October 2023

Communicated by Francesco dell'Isola
Authors
Oleksiy Kapustyan
Taras Shevchenko National University
Kyiv
01601
Ukraine
Olena Kapustian
Taras Shevchenko National University
Kyiv
01601
Ukraine
Ihor Korol
Uzhhorod National University
Uzhhorod
88000
Ukraine
John Paul II Catholic University
Lublin
20-708
Poland
Bruno Rubino
Department of Information Engineering, Computer Science and Mathematics
University of L’Aquila
67100 L’Aquila
Italy