Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Upper Estimate for Hausdorff Dimension of Invariant Sets of Evolutionary Variational Inequalities

Author(s):

Amina V. Kruck

Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics
198504, Peterhof, St. Petersburg, Russia
Universitetsky prospekt, 28

kruck.amina@gmail.com

Abstract:

In this paper we consider a class of evolutionary variational inequalities arising in mechanics. The method of determining observations is used to obtain upper estimates for fractal and Hausdorff dimension of invariant sets of variational inequalities. The construction of determining observation is realised by frequency theorem for evolution systems (Theorem Likhtarnikov-Yakubovich). A similar approach for the construction of determining observation was used to investigate the system stability and the existence of attractor of evolution systems. The main result of this paper is frequency conditions for the existence of determining observation, which allow us to obtain upper estimates for fractal and the Hausdorff dimension of an invariant set. As an example we show how to apply the obtained results to the investigation of viscoelasticity contact problem.

Keywords

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