Existence and stability of pullback exponential attractors for a class of non-autonomous reaction-diffusion equations

The aim of this work is to investigate and prove the existence and stability of a family of pullback exponential attractors for a general class of non-autonomous reaction-diffusion equations. In other words, we prove the upper and lower-semicontinuity of this family of pullback exponential attractors, and we also guarantee the existence of a finite-dimensional (with respect to the fractal dimension) pullback attractor that is upper-semicontinuous. We highlight that, to achieve the results described above, we use in this paper a general theoretical criterion based on a smoothing condition. This criterion is well suited to parabolic-type problems such as the one we are interested in, and it proves the stability of the pullback exponential attractors with respect to a parameter $ \epsilon $, contributing to a deeper understanding of the asymptotic behavior of solutions to this model.