Smooth attractor for a nonlinear thermoelastic diffusion thin plate based on Gurtin–Pipkin’s model

Abstract

A nonlinear system of sixth-order evolution equations which takes into account the hereditary effects via Gurtin- Pipkin's model and the rotational inertia is considered. The system describes the behavior of thermoelastic diffusion thin plates, recently derived by Aouadi (Applied Mathematics and Mechanics (English Edition) 36 (2015), 619-632), where the heat and diffusion fluxes depend on the past history of the temperature and diffusion gradients through memory kernels, respectively. We prove the existence and uniqueness of global solutions as well as the exponential stability of the linear system at a rate proportional to the rotational inertia parameter. The existence of a global attractor whose fractal dimension is finite is proved. Finally, a smoothness property of the attractor is established with respect to the rotational inertia parameter.