On a class of differential quasi-variational-hemivariational inequalities in infinite-dimensional Banach spaces
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Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation
doi: 10.3934/eect.2021054
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Robustness of global attractors: Abstract framework and application to dissipative wave equations
Sergey Dashkovskiy 1,, and Oleksiy Kapustyan 2,
University of Würzburg, Institute of Mathematics, Emil-Fischer-Straße 40, 97074 Würzburg, Germany
Taras Shevchenko National University of Kyiv, Department of Mathematics and Mechanics, Volodymyrska Street 64, 01601 Kyiv, Ukraine
* Corresponding author: Sergey Dashkovskiy
Received March 2021 Revised July 2021 Early access October 2021
Fund Project: This work is partially supported by the German Research Foundation (DFG) grant DA 767/12-1 and the National Research Foundation of Ukraine (NRFU) through the joint German-Ukrainian grant "Stability and robustness of attractors of nonlinear infinite-dimensional systems with respect to disturbances"
We establish local input-to-state stability and the asymptotic gain property for a class of infinite-dimensional systems with respect to the global attractor of the respective undisturbed system. We apply our results to a large class of dissipative wave equations with nontrivial global attractors.
Keywords: Input-to-state stability, asymptotic gain, global attractor, infinite-dimensional system, nonlinear wave equation.
Mathematics Subject Classification: Primary: 35B40, 35B41, 93B35; Secondary: 93D09, 35B35, 35L05.
Citation: Sergey Dashkovskiy, Oleksiy Kapustyan. Robustness of global attractors: Abstract framework and application to dissipative wave equations. Evolution Equations & Control Theory, doi: 10.3934/eect.2021054
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Sergey Dashkovskiy Oleksiy Kapustyan