Long-time behavior of solutions for quasilinear hyperbolic hemivariational inequalities with application to piezoelectricity problem

We consider quasilinear autonomous inclusions of hyperbolic type. The dynamics of all weak solutions defined on the positive semi-axis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. The classes of mathematical models for piezoelectric...

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Bibliographic Details
Published in:Applied mathematics letters 2012-10, Vol.25 (10), p.1569-1574
Main Authors: Zgurovsky, Michael Z., Kasyanov, Pavlo O., Zadoianchuk (Zadoyanchuk), Nina V.
Format: Article
Language:English
Subjects:
Attractor
Hemivariational inequality
Inclusion
Piezoelectricity
PZT-4
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Summary:We consider quasilinear autonomous inclusions of hyperbolic type. The dynamics of all weak solutions defined on the positive semi-axis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. The classes of mathematical models for piezoelectric fields containing the multidimensional law are studied. The conditions of the output of each weak solution for this problem at stationary states are given. We consider as a particular case the piezoelectric model for PZT-4 piezoceramics as one of the possible applications.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2012.01.016