Global and exponential attractors for extensible thermoelastic plate with time-varying delay

A class of nonlinear problems modeling thermoelastic extensible plates with rotational inertia and time-dependent delay in the internal feedback are considered. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of global solution. The proof with or without rotational inertia, does not depend on the parameters gamma(1) and gamma(2) of time-dependent delay. Moreover, the existence of compact global and exponential attractors is proved through a stabilizability estimate. This estimate which is established under restrictions on gamma(1) and gamma(2) and independently of the rotational inertia parameter (omega) over bar, provides bounds on the attractors' fractal dimension. Other property such as additional smoothness of global attractors with respect to parameter (omega) over bar is also presented. Furthermore, the existence of a generalized fractal exponential attractor is also derived. Finally, we show that the family of global attractors is continuous with respect to the parameter (omega) over bar in some sense. (c) 2020 Elsevier Inc. All rights reserved.