@misc{10481/75199,
year = {2022},
month = {4},
url = {http://hdl.handle.net/10481/75199},
abstract = {This paper proposes a review focused on exotic chemotaxis and cross-diffusion models
in complex environments. The term exotic is used to denote the dynamics of models
interacting with a time-evolving external system and, specifically, models derived with
the aim of describing the dynamics of living systems. The presentation first, considers
the derivation of phenomenological models of chemotaxis and cross-diffusion models
with particular attention on nonlinear characteristics. Then, a variety of exotic models
is presented with some hints toward the derivation of new models, by accounting for a
critical analysis looking ahead to perspectives. The second part of the paper is devoted to
a survey of analytical problems concerning the application of models to the study of real
world dynamics. Finally, the focus shifts to research perspectives within the framework
of a multiscale vision, where different paths are examined to move from the dynamics
at the microscopic scale to collective behaviors at the macroscopic scale.},
organization = {Spanish Government	RTI2018-098850-B-I00},
organization = {Junta de Andalucia
European Commission	PY18-RT-2422	
A-FQM-311-UGR18	
B-FQM-580-UGR20},
organization = {National Natural Science Foundation of China (NSFC)	12171316},
organization = {Shanghai Frontiers Science Center of Modern Analysis},
organization = {German Research Foundation (DFG)	411007140},
organization = {GZ: WI 3707/5-1},
publisher = {World Scientific},
keywords = {Keller–Segel},
keywords = {Cross diffusion},
keywords = {Multiscale problems},
keywords = {Pattern formation},
keywords = {Complex interactions},
keywords = {Blow-up},
keywords = {Well-posedness},
keywords = {Micro-macro derivation},
title = {Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision},
doi = {10.1142/S0218202522500166},
author = {Bellomo, Nicola and Soler Vizcaino, Juan Segundo},
}