# American Institute of Mathematical Sciences

September  2015, 4(3): 241-263. doi: 10.3934/eect.2015.4.241

## Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory

 1 Ecole Nationale d'Ingénieurs de Bizerte, Université de Carthage, BP66, Campus Universitaire Menzel Abderrahman 7035, Tunisia 2 Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, 86962 Chasseneuil Futuroscope Cedex

Received  February 2015 Revised  April 2015 Published  September 2015

We analyse the longterm properties of a $C_0-$semigroup describing the solutions to a nonlinear thermoelastic diffusion plate, recently derived by Aouadi [1], where the heat and diffusion flux depends on the past history of the temperature and the chemical potential gradients through memory kernels. First we prove the well-posedness of the initial-boundary-value problem using the $C_0-$semigroup theory of linear operators. Then we show, without rotational inertia, that the thermal and chemical potential coupling is strong enough to guarantee the quasi-stability. By showing that the system is gradient and asymptotically compact, the existence of a global attractor whose fractal dimension is finite is proved.
Citation: Moncef Aouadi, Alain Miranville. Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Evolution Equations & Control Theory, 2015, 4 (3) : 241-263. doi: 10.3934/eect.2015.4.241
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