Geodesic
Wright–Fisher–type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities
Furioli, Giulia1 ; Pulvirenti, Ada2 ; Terraneo, Elide3 ; Toscani, Giuseppe2
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
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 2065-2082

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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.

DOI : 10.1016/j.anihpc.2019.07.005
Keywords: Fokker-Planck type equations, Large time behavior, Weighted Logarithmic-Sobolev inequalities

Furioli, Giulia 1 ; Pulvirenti, Ada 2 ; Terraneo, Elide 3 ; Toscani, Giuseppe 2

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 
@article{AIHPC_2019__36_7_2065_0,
     author = {Furioli, Giulia and Pulvirenti, Ada and Terraneo, Elide and Toscani, Giuseppe},
     title = {Wright{\textendash}Fisher{\textendash}type equations for opinion formation, large time behavior and weighted {logarithmic-Sobolev} inequalities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2065--2082},
     publisher = {Elsevier},
     volume = {36},
     number = {7},
     year = {2019},
     doi = {10.1016/j.anihpc.2019.07.005},
     mrnumber = {4020534},
     zbl = {1434.35238},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.07.005/}
}
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Furioli, Giulia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe. Wright–Fisher–type equations for opinion formation, large time behavior and weighted logarithmic-Sobolev inequalities. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 2065-2082. doi: 10.1016/j.anihpc.2019.07.005

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