@article{Shi2024, 
author = {Yadan Shi and Yongqin Xie and Ke Li and Zhipiao Tang},
title = {Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {12},
pages = {6847-6868},
keywords = {nonclassical diffusion equation, pullback attractors, nonlinear delay, polynomial growth},
url = {https://www.sciopen.com/article/10.3934/era.2024320},
doi = {10.3934/era.2024320},
abstract = {In this study, we primarily investigate the asymptotic behavior of solutions associated with a nonclassical diffusion process by memory effects and a perturbed parameter that varies over time. A significant innovation is the consideration of a delay term governed by a function with minimal assumptions: merely measurability and a phase-space that is a time-dependent space of continuously-time-varying functions. By employing a novel analytical approach, we demonstrate the existence and regularity of time-varying pullback  D-attractors. Notably, the nonlinearity  f is unrestricted by any upper limit on its growth rate.}
}