Open AccessRobustness of global attractors: Abstract framework and application to dissipative wave equations
Author(s) -
Sergey Dashkovskiy,
O. V. Kapustyan
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2021054
Subject(s) - attractor , dissipative system , robustness (evolution) , class (philosophy) , mathematics , mathematical analysis , exponential stability , stability (learning theory) , property (philosophy) , physics , statistical physics , computer science , nonlinear system , quantum mechanics , biochemistry , chemistry , philosophy , epistemology , artificial intelligence , machine learning , gene
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.