The quasi-invariant limit for a kinetic model of sociological collective behavior

Laurent Boudin (1, 2) , Francesco Salvarani (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 REO - Numerical simulation of biological flows
3 Dipartimento di matematica F. Casorati

The paper is devoted to the study of the asymptotic behaviour of a kinetic model proposed to forecast the phenomenon of opinion formation, with both effect of self-thinking and compromise between individuals. By supposing that the effects of self-thinking and compromise are very weak, we deduce, asymptotically, some simpler models who lose the kinetic structure. We explicitly characterize the asymptotic state of the limiting equation and study the speed of convergence towards equilibrium.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Boudin, Francesco Salvarani. The quasi-invariant limit for a kinetic model of sociological collective behavior. Kinetic and Related Models , 2009, pp.433-449. ⟨10.3934/krm.2009.2.433⟩. ⟨hal-00357592⟩