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

Tamara Fastovska

doi:10.3934/cpaa.2007.6.83

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2007, Volume 6, Issue 1: 83-101. Doi: 10.3934/cpaa.2007.6.83

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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

Received: January 31, 2006

Revised: June 30, 2006

Published: February 2007

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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.

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Mathematics Subject Classification: Primary: 35B25, 35B40; Secondary: 37L30, 45K05.

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

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