# American Institute of Mathematical Sciences

July  2017, 22(5): 1875-1886. doi: 10.3934/dcdsb.2017111

## Global attractors of impulsive parabolic inclusions

 1 Institute of Mathematics, University of Würzburg, Emil-Fischer-Straße 40, Würzburg, Germany 2 Taras Shevchenko National University of Kyiv, Department of Mathematics and Mechanics, Volodymyrska Str. 60,01033, Kyiv, Ukraine

* Corresponding author: O. Kapustyan

This work is supported by the German Research Foundation (DFG) via grant DA 767/8-1 The second author is also supported by the State Fund For Fundamental Research, Grant of President of Ukraine, Project F62/94-2015.

Received  November 2015 Revised  March 2016 Published  March 2017

In this work we consider an impulsive multi-valued dynamical system generated by a parabolic inclusion with upper semicontinuous right-hand side $\varepsilon F(y)$ and with impulsive multi-valued perturbations. Moments of impulses are not fixed and defined by moments of intersection of solutions with some subset of the phase space. We prove that for sufficiently small value of the parameter $\varepsilon>0$ this system has a global attractor.

Citation: Sergey Dashkovskiy, Oleksiy Kapustyan, Iryna Romaniuk. Global attractors of impulsive parabolic inclusions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1875-1886. doi: 10.3934/dcdsb.2017111
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