Explicit solution of the nonlinear Vlasov equation using the subdynamics approach

1989 ◽  
Vol 156 (2) ◽  
pp. 651-678 ◽  
Author(s):  
V. Škarka
Keyword(s):  
Vlasov Equation ◽  
Explicit Solution

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals The explicit solution to a sequential switching problem with non-smooth data

Stochastics ◽  
2010 ◽  
Vol 82 (1) ◽  
pp. 69-109 ◽  
Author(s):  
Timothy C. Johnson ◽  
Mihail Zervos
Keyword(s):  
Explicit Solution ◽  
Sequential Switching ◽  
Smooth Data
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