On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis

This paper develops an asymptotic theory for a large class of Boltzmann type equations suitable to model the evolution of multicellular systems in biology with special attention to the onset of nonlinear phenomena. The mathematical method shows how various levels of diffusion phenomena, linear and non-linear, can be obtained by suitable asymptotic limits. The time scaling corresponding to different speeds related to cell movement and biological evolution plays a crucial role and different macroscopic equations corresponds to different scaling.