Speed of convergence to equilibrium in Wasserstein metrics for Kac-s like kinetic equations

Large deviations for the solution of a Kac-type kinetic equation

“…Convergence to self-similar solutions. In the study of the asymptotic behavior of the solutions of (1), a fundamental role is played by the fixed point equation for distributions (6)…”

“…As for the speed of convergence to equilibrium, explicit rates with respect to suitable probability metrics have been derived in various papers. For the Kac equation see [13,14,17], for the inelastic Kac equation see [4], for the solutions of the general model ( 1)-( 2) see [2,3,6].…”