The quasi-invariant limit for a kinetic model of sociologicalcollective behavior

Laurent Boudin; Francesco Salvarani

doi:10.3934/krm.2009.2.433

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2009, Volume 2, Issue 3: 433-449. Doi: 10.3934/krm.2009.2.433

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

Laurent Boudin^1, and
Francesco Salvarani^2,

1.
UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005
2.
Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1 - 27100 Pavia

Received: December 31, 2008

Revised: May 31, 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 82C22; Secondary: 91D10.

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