ABSTRACT
In this article, we investigate a class of non-autonomous semi-linear second-order evolution with memory terms, expressed by the convolution integrals, which account for the past history of one or more variables. First, the asymptotic regularity of solutions is proved, while the nonlinearity is critical and the time-dependent external forcing term is assumed to be only translation-bounded (instead of translation-compact), and then the existence of compact uniform attractors together with its structure and regularity is established. Finally, the existence of robust family of exponential attractors is constructed.
Acknowledgements
The authors want to express their sincere gratitude to the anonymous reviewers for their careful reading of the paper, giving us valuable comments and suggestions. They also thank the editors for their kind help.
Disclosure statement
No potential conflict of interest was reported by the authors.