On Villani's conjecture concerning entropy production for the Kac Master equation

Pages: 479 - 497, Volume 4, Issue 2, June 2011

doi:10.3934/krm.2011.4.479       Abstract        References        Full Text (223.7K)       Related Articles

Amit Einav - Department of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States (email)

Abstract: In this paper we take an idea presented in recent paper by Carlen, Carvalho, Le Roux, Loss, and Villani ([3]) and push it one step forward to find an exact estimation on the entropy production. The new estimation essentially proves that Villani's conjecture is correct, or more precisely that a much worse bound to the entropy production is impossible in the general case.

Keywords:  Entropy production, Villani's conjecture.
Mathematics Subject Classification:  Primary: 70F99, 60J25.

Received: September 2010;      Revised: February 2011;      Published: April 2011.

 References