Communications on Pure and Applied Analysis (CPAA)

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

Pages: 83 - 101, Volume 6, Issue 1, March 2007      doi:10.3934/cpaa.2007.6.83

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Tamara Fastovska - Department of Mathematics and Mechanics, Kharkiv National University, Svobody sq. 4, 61077 Kharkiv, Ukraine (email)

Abstract: 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:  Thermoelasticity with memory, global attractors, fractal dimension, upper semicontinuity.
Mathematics Subject Classification:  Primary: 35B25, 35B40; Secondary: 37L30, 45K05.

Received: February 2006;      Revised: July 2006;      Published: December 2006.