Wright–Fisher–type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities

We study the rate of convergence to equilibrium of the solution of a Fokker–Planck type equation introduced in [19] 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.