American Institute of Mathematical Sciences

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January  2010, 9(1): 161-192. doi: 10.3934/cpaa.2010.9.161

Asymptotic behavior of thermoviscoelastic Berger plate

Mykhailo Potomkin 1,

1. 

Kharkiv National University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkiv, Ukraine

Received  January 2009 Revised  May 2009 Published  October 2009

System of partial differential equations with convolution terms and non-local nonlinearity describing oscillations of plate due to Berger's approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and fading memory of material is considered. The equation is transformed into a dynamical system in a suitable Hilbert space, which asymptotic behavior is analysed. Existence of a compact global attractor in this dynamical system and some of its properties are proved in this paper. Main tool in analysis of asymptotic behavior is stabilizability inequality.
Keywords: global attractor, linear memory., Coupled PDE system.
Mathematics Subject Classification: 35B40, 35B4.
Citation: Mykhailo Potomkin. Asymptotic behavior of thermoviscoelastic Berger plate. Communications on Pure & Applied Analysis, 2010, 9 (1) : 161-192. doi: 10.3934/cpaa.2010.9.161
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