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Department of Integral and Differential Equations, Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 60, 01601 Kyiv, Ukraine
Department of System Analysis and Decision Making Theory, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 60, 01601 Kyiv, Ukraine and Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Universita degli Studi dell’Aquila, Via Vetorio, Coppito 1, 67100 L’Aquila, Italy
Department of General Mathematics, Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 60, 01601 Kyiv, Ukraine
Department of Algebra and Differential Equations, Faculty of Mathematics and Digital Technologies, Uzhhorod National University, Narodna Square, 3, 88000 Uzhhorod, Ukraine and Department of Mathematical Analysis, Faculty of Natural Sciences and Health, The John Paul II Catholic University of Lublin, Al. Raclawickie 14, 20-950 Lublin, Poland
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Abstract: In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.
AMSclassification: primary 26A12; secondary 34C10.
Keywords: parabolic equations, attractor, stability.
DOI: 10.5817/AM2023-2-191