# American Institute of Mathematical Sciences

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On relation between attractors for single and multivalued semiflows for a certain class of PDEs
March  2019, 24(3): 1229-1242. doi: 10.3934/dcdsb.2019013

## Attractors of multivalued semi-flows generated by solutions of optimal control problems

 1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine 2 Institute for Applied System Analysis, National Technical University "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine 3 Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202-Elche, Alicante, Spain 4 National Technical University "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine

To Professor Valery Melnik, in Memoriam

Received  February 2018 Revised  June 2018 Published  January 2019

Fund Project: The first two authors were partially supported by the State Fund for Fundamental Research of Ukraine under grants GP/F66/14921, GP/F78/187 and by the Grant of the National Academy of Sciences of Ukraine 2290/2018. The third author was partially supported by Spanish Ministry of Economy and Competitiveness and FEDER, projects MTM2015-63723-P and MTM2016-74921-P, and by Junta de Andalucía(Spain), project P12-FQM-1492.

In this paper we study the dynamical system generated by the solutions of optimal control problems. We obtain suitable conditions under which such systems generate multivalued semiprocesses. We prove the existence of uniform attractors for the multivalued semiprocess generated by the solutions of controlled reaction-diffusion equations and study its properties.

Citation: Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Mikhail Z. Zgurovsky. Attractors of multivalued semi-flows generated by solutions of optimal control problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1229-1242. doi: 10.3934/dcdsb.2019013
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