Exponential convergence to equilibrium of solutions of the Kac equation and homogeneous Boltzmann equation for Maxwellian without angular cut-off

2017 ◽  
Vol 101 (4) ◽  
pp. 251-271
Author(s):  
Fei Meng ◽  
Xiao-Ping Yang
Keyword(s):  
Boltzmann Equation ◽  
Exponential Convergence ◽  
Convergence To Equilibrium ◽  
Homogeneous Boltzmann Equation ◽  
Kac Equation

scholarly journals SPATIALLY HOMOGENEOUS MAXWELLIAN MOLECULES IN A NEIGHBORHOOD OF THE EQUILIBRIUM

2014 ◽  
Author(s):  
Emanuele Dolera
Keyword(s):  
Boltzmann Equation ◽  
Exponential Convergence ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Homogeneous Boltzmann Equation ◽  
Long Time ◽  
Spatially Homogeneous ◽  
Maxwellian Molecules ◽  
Spatially Homogeneous Boltzmann Equation

This note deals with the long-time behavior of the solution to the spatially homogeneous Boltzmann equation for Maxwellian molecules, when the initial datum belongs to a suitable neighborhood of the Maxwellian equilibrium. In particular, it contains a quantification of the rate of exponential convergence, obtained by simple arguments.

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