Cross-diffusion models in complex frameworks from microscopic to macroscopic

This paper deals with the micro–macro derivation of models from underlying description provided by methods kinetic theory for active particles. We consider so-called exotic according to definition proposed in [ N. Bellomo, Outada, J. Soler, Y. Tao and M. Winkler, Chemotaxis cross diffusion complex environments: Modeling towards a multiscale vision, Math. Models Methods Appl. Sci. 32 (2022) 713–792]. The first part presentation focuses on survey critical analysis some phenomenological known literature. refer selection case studies, detail, transport virus models, social dynamics, Keller–Segel fluid. second shows how Hilbert-type approach can be developed derive at macroscale third macroscopic corresponding selected studies. Finally, forward look into future research perspectives is proposed.