Abstract and Applied Analysis
Volume 2012 (2012), Article ID 450984, 21 pages
http://dx.doi.org/10.1155/2012/450984
Research Article

Long-Time Behaviour of Solutions for Autonomous Evolution Hemivariational Inequality with Multidimensional “Reaction-Displacement” Law

Pavlo O. Kasyanov,1 Luisa Toscano,2 and Nina V. Zadoianchuk1

1Institute for Applied System Analysis NAS of Ukraine, Peremogy Avenue 37, Building 35, Kyiv 03056, Ukraine
2Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Claudio 21, 80125 Naples, Italy

Received 2 December 2011; Accepted 27 January 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Pavlo O. Kasyanov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider autonomous evolution inclusions and hemivariational inequalities with nonsmooth dependence between determinative parameters of a problem. The dynamics of all weak solutions defined on the positive semiaxis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. New properties of complete trajectories are justified. We study classes of mathematical models for geophysical processes and fields containing the multidimensional “reaction-displacement” law as one of possible application. The pointwise behavior of such problem solutions on attractor is described.