Attracting sets in sup-norms for mild solutions of impulsive-perturbed parabolic semilinear problems
Kapustyan O. Temesheva S. Tleulessova A.
2025American Institute of Mathematical Sciences
AIMS Mathematics
2025#10Issue 819173 - 19188 pp.
In this paper, we investigate the qualitative behavior of an evolutionary problem that consists of a semilinear parabolic equation whose trajectories undergo instantaneous impulsive perturbations at the moments when some integral functional reaches a certain threshold value. The key object is the uniform attractor of the corresponding impulsive infinite-dimensional dynamical system. The novelty of this study is the analysis of mild solutions in the phase space of continuous functions. Under general assumptions on the impulsive parameters, we prove that this problem generates an impulsive dynamical system, and its trajectories have a compact uniform attractor with respect to the supremum norm (sup-norm).
compact limit dynamics , global attractors , impulsive dynamical systems , impulsive perturbations , mild solutions , phase space , semilinear parabolic equations , sup-norm , uniform attractors
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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, Almaty, Kazakhstan
Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Fundamental Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Faculty of Mechanics and Mathematics
Department of Mathematics
Department of Differential Equations
Department of Fundamental Mathematics
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