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March  2007, 6(1): 83-101. doi: 10.3934/cpaa.2007.6.83

Upper semicontinuous attractor for 2D Mindlin-Timoshenko thermoelastic model with memory

Tamara Fastovska 1,

1. 

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

Received  February 2006 Revised  July 2006 Published  December 2006

A nonlinear problem for thermoelastic Mindlin-Timoshenko plate with hereditary heat conduction of Gurtin-Pipkin type is considered here. We prove the existence of a compact global attractor whose fractal dimension is finite. The main aim of the work is to show the upper semicontinuity of the attractor as the relaxation time tends to zero.
Keywords: fractal dimension, global attractors, upper semicontinuity., Thermoelasticity with memory.
Mathematics Subject Classification: Primary: 35B25, 35B40; Secondary: 37L30, 45K0.
Citation: Tamara Fastovska. Upper semicontinuous attractor for 2D Mindlin-Timoshenko thermoelastic model with memory. Communications on Pure and Applied Analysis, 2007, 6 (1) : 83-101. doi: 10.3934/cpaa.2007.6.83
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