Asymptotic analysis of continuous opinion dynamics models under bounded confidence

This paper deals with the asymptotic behavior of mathematical models for opinion dynamics under bounded confidence of Deffuant-Weisbuch type.Focusing on the Cauchy Problem related to compromise models with homogeneous bound of confidence, a general well-posedness result is provided and a systematic study of the asymptotic behavior in time of the solution is developed. More in detail, we prove a theorem that establishes the weak convergence of the solution to a sum of Dirac masses and characterizes the concentration points for different values of the model parameters. Analytical results are illustrated by means of numerical simulations.