Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision
MetadataShow full item record
Keller–SegelCross diffusionMultiscale problemsPattern formationComplex interactionsBlow-upWell-posednessMicro-macro derivation
Bellomo, N... [et al.] (2022). Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. Mathematical Models and Methods in Applied Sciences, 32(04), 713-792. DOI: [10.1142/S0218202522500166]
SponsorshipSpanish Government RTI2018-098850-B-I00; Junta de Andalucia European Commission PY18-RT-2422 A-FQM-311-UGR18 B-FQM-580-UGR20; National Natural Science Foundation of China (NSFC) 12171316; Shanghai Frontiers Science Center of Modern Analysis; German Research Foundation (DFG) 411007140; GZ: WI 3707/5-1
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.