Kinetic and Related Models (KRM)

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

Pages: 433 - 449, Volume 2, Issue 3, September 2009      doi:10.3934/krm.2009.2.433

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Laurent Boudin - UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005, France (email)
Francesco Salvarani - Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1 - 27100 Pavia, Italy (email)

Abstract: The paper is devoted to the study of the asymptotic behavior 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 asymptotically deduce some simpler models who loose the kinetic structure. We explicitly characterize the asymptotic state of the limiting equation and study the speed of convergence towards equilibrium.

Keywords:  Sociophysics, opinion formation, kinetic theory.
Mathematics Subject Classification:  Primary: 82C22; Secondary: 91D10.

Received: January 2009;      Revised: June 2009;      Available Online: July 2009.