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We study the rate of convergence to equilibrium of the solution of a Fokker–Planck type equation introduced in  to describe opinion formation in a multi-agent system. The main feature of this Fokker–Planck equation is the presence of a variable diffusion coefficient and boundaries, which introduce new challenging mathematical problems in the study of its long-time behavior.
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Giulia Furioli, Ada Pulvirenti, Elide Terraneo, Giuseppe Toscani, Wright–Fisher–type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, pp. 2065–2082DOI 10.1016/J.ANIHPC.2019.07.005