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

Abstract

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.