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Wright–Fisher–type equations for opinion formation,large time behavior and weighted logarithmic-Sobolev inequalities
Institution:1. DIGIP, University of Bergamo, viale Marconi 5, 24044 Dalmine, Italy;2. Department of Mathematics, University of Pavia, via Ferrata 1, Pavia, 27100 Italy;3. Department of Mathematics, University of Milan, via Saldini 50, 20133 Milano, Italy;1. Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic;2. Mathematical Institute, University of Oxford, UK;3. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland;4. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic;1. CNRS, Sorbonne Université, Laboratoire Jacques-Louis Lions, UMR 7598, Boite courrier 187, 75252, Paris Cedex 05, France;2. ULCO, LMPA J. Liouville, BP 699, F-62228 Calais, France;3. CNRS FR 2956, France;1. The University of Texas at Austin, Department of Mathematics – RLM 8.100, 2515 Speedway – Stop C1200, Austin, TX 78712-1202, United States of America;2. CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal;3. Purdue University, Department of Mathematics, 150 N. University Street, West Lafayette, IN 47907-2067, United States of America
Abstract: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.
Keywords:Fokker-Planck type equations  Large time behavior  Weighted Logarithmic-Sobolev inequalities
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