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We present and discuss various one-dimensional linear Fokker–Planck-type equations that have been recently considered in connection with the study of interacting multi-agent systems. In general, these Fokker–Planck equations describe the evolution in time of some probability density of the population of agents, typically the distribution of the personal wealth or of the personal opinion, and are mostly obtained by linear or bilinear kinetic models of Boltzmann type via some limit procedure. The main feature of these equations is the presence of variable diffusion, drift coefficients and boundaries, which introduce new challenging mathematical problems in the study of their long-time behavior.
Furioli et al. (Fri,) studied this question.