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

Author

Listed:
  • Pavlo O. Kasyanov
  • Luisa Toscano
  • Nina V. Zadoianchuk

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.

Suggested Citation

  • Pavlo O. Kasyanov & Luisa Toscano & Nina V. Zadoianchuk, 2012. "Long‐Time Behaviour of Solutions for Autonomous Evolution Hemivariational Inequality with Multidimensional “Reaction‐Displacement” Law," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:450984
    DOI: 10.1155/2012/450984
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    References listed on IDEAS

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    1. D. Goeleven & M. Miettinen & P. D. Panagiotopoulos, 1999. "Dynamic Hemivariational Inequalities and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 567-601, December.
    2. Muhammad Aslam Noor, 2012. "Some Aspects of Extended General Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Syed Tauseef Mohyud-Din & Muhammad Aslam Noor & Khalida Inayat Noor, 2009. "Some Relatively New Techniques for Nonlinear Problems," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-25, July.
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