The existence of classical solution for the Fokker-Planck-Boltzmann equation

2010 ◽  
Author(s):  
Yin Xunwu
Keyword(s):  
Boltzmann Equation ◽  
Classical Solution ◽  
Fokker Planck

THE GLOBAL CLASSICAL SOLUTION OF THE VLASOV–MAXWELL–FOKKER–PLANCK SYSTEM NEAR MAXWELLIAN

2011 ◽  
Vol 21 (05) ◽  
pp. 1007-1025 ◽  
Author(s):  
MYEONGJU CHAE
Keyword(s):  
Cauchy Problem ◽  
Electromagnetic Field ◽  
Classical Solution ◽  
Charged Particles ◽  
Classical Solutions ◽  
Global Classical Solution ◽  
Self Consistent ◽  
The Cauchy Problem ◽  
Fokker Planck

The Vlasov–Maxwell–Fokker–Planck system is used in modeling distribution of charged particles in plasma, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of global in time classical solutions to the Cauchy problem near Maxwellians.

An analytical solution to the Boltzmann–Fokker–Planck equation for multi-component non-homogeneous plasmas

1989 ◽  
Vol 41 (3) ◽  
pp. 457-467 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman
Keyword(s):  
Boltzmann Equation ◽  
Energy Exchange ◽  
Collision Operator ◽  
Planck Equation ◽  
Large Temperature ◽  
Relaxation Rates ◽  
Plasma Model ◽  
Slowing Down ◽  
Component Plasma ◽  
Fokker Planck

The previously obtained analytical solution to the Boltzmann equation for nonhomogeneous plasmas with relative large temperature and density gradients is generalized in the following sense. (i) The relatively simple Bhatnagar, Gross and Krook collision operator is replaced by the Fokker-Planck operator expressed in terms of relaxation rates (slowing down, energy exchange, etc.). (ii) The simple Lorentzian plasma model is replaced by a multi-component plasma model with realistic masses and temperatures.

Sign in / Sign up

Export Citation Format

Share Document