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Regular version of the site

Article

Регулярные аттракторы автономных и неавтономных динамических систем

Доклады Академии наук. 2014. Т. 455. № 5. С. 512-517.
Зелик С. В., Чепыжов В. В.
Translator: О. Сипачева
Editor of translation: В. А. Ильин

We study regular global attractors of the dynamical systems corresponding to dissipative evolution equations and their nonautonomous perturbations. We prove that the nonautonomous dynamical system (process) resulting from a small nonautonomous perturbation of an autonomous dynamical system (semigroup) having a regular attractor has a regular nonautonomous attractor as well. Moreover, the symmetric Hausdorff deviation of the perturbed attractors from the unperturbed ones is bounded above by O(ε^κ), where ε is a perturbation parameter and 0 < κ < 1. We apply the obtained results to weakly dissipative wave equations in a bounded domain in the three-dimensional space perturbed by timedependent external forces.