Global attractors of impulsive parabolic inclusions

Sergey Dashkovskiy; Oleksiy Kapustyan; Iryna Romaniuk

doi:10.3934/dcdsb.2017111

Article Contents

2017, Volume 22, Issue 5: 1875-1886. Doi: 10.3934/dcdsb.2017111

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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
* Corresponding author: O. Kapustyan

Received: November 2015

Revised: March 2016

Published online: March 2017

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Abstract

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.

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Mathematics Subject Classification: Primary:35B40, 35B41;Secondary:35K55, 58C06.

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References

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