Asymptotic behavior of impulsive parabolic problem with infinite-dimensional impulsive set
Kapustyan O. Fedorenko J. Temesheva S.
1 October 2025Walter de Gruyter GmbH
Georgian Mathematical Journal
2025#32Issue 5859 - 868 pp.
In the paper we consider semilinear parabolic equation with a nonlinear term εf(u), whose trajectories undergo impulsive perturbations when they meet the impulsive set M={∥u∥=R}. We prove that for sufficiently small ε this problem generates an impulsive dynamical system which possesses a compact uniform attractor in the phase space L2.
asymptotic stability , attractors in phase space , compact uniform attractor , evolutionary equations theory , hybrid systems , Impulsive dynamical systems , impulsive perturbations , infinite-dimensional phase space , nonlinear dynamical systems , semilinear parabolic equations
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Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Department of Mathematics, Al-Farabi Kazakh National University, Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Faculty of Mechanics and Mathematics
Department of Mathematics
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