Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 46, pp. 1-21.

Title: Asymptotic behavior of linearized Boltzmann equations for soft potentials with cut-off
       
Authors: Yakui Wu (Capital Normal Univ., Beijing, China)
         Jiawei Sun (Shandong Normal Univ., Jinan, China)

Abstract: 
 We consider the asymptotic behavior of the linearized Boltzmann equation for
 soft potentials with cut-off. By introducing a new decomposition of the linearized
 Boltzmann operator, we analyze the spectrum of the linearized Boltzmann operator and
 obtain the asymptotic behaviors of the linearized Boltzmann equation for γ in (-3,0),
 extending the result in [12] for γ in (-1,0).

Submitted December 9, 2020. Published May 27, 2021.
Math Subject Classifications: 76P05, 35B20, 35B40, 35P20.
Key Words: Linearized Boltzmann operator; soft potentials; spectrum; semigroup;
           time decay; estimates.