Zgurovsky, M.Z., D’Apice, C., De Maio, U., Gorban N.V., Kasyanov P.O., Kapustyan O.V., Khomenko, O.V., Valero, J. (2021) «Uniform Global Attractor for a Class of Nonautonomous Evolution Hemivariational Inequalities with Multidimensional “Reaction-Velocity” Law», in Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, Sadovnichiy, V.A., Zgurovsky, V.A. (Eds), Understanding Complex Systems, Springer, 347-368

Michael Z. Zgurovsky (National Technical University of Ukraine “Igor Sikorsky Kyiv Politechnic Institute”), Ciro D’Apice (Dipartimento di Science Aziendali-Management e Innovation Systems, University of Salerno), Umberto De-Maio (Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”), Pavlo O. Kasyanov, Olha V. Khomenko (Institute for Applied System Analysis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”), O. V. Kapustyan (Taras Shevchenko National University of Kyiv, Institute for Applied System Analysis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”) and José Valero (Centro de Investigación Operativa, Universidad Miguel Hernandez de Elche)

Abstract: We consider non-autonomous evolution inclusions and hemivariation inequalities with possibly non-monotone multidimensional “reaction-velocity” law. The dynamics of all weak solutions defined on the positive semi-axis of time is investigated. We prove the existence global attractor. New properties of complete trajectories are justified. The pointwise behavior of such problem solutions on attractor is described in the autonomous case.