Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory
Moncef Aouadi - Ecole Nationale d'Ingénieurs de Bizerte, Université de Carthage, BP66, Campus Universitaire Menzel Abderrahman 7035, Tunisia (email)
Abstract: We analyse the longterm properties of a $C_0-$semigroup describing the solutions to a nonlinear thermoelastic diffusion plate, recently derived by Aouadi , 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.
Keywords: Thermoelastic diffusion plate, memory, global solutions, global attractor.
Received: February 2015; Revised: April 2015; Available Online: September 2015.
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