Application of spectral deformation to the Vlasov–Poisson system. II. Mathematical results

1989 ◽  
Vol 30 (12) ◽  
pp. 2819-2837 ◽  
Author(s):  
Peter D. Hislop ◽  
John David Crawford
Keyword(s):  
Poisson System ◽  
Spectral Deformation

Application of the method of spectral deformation to the Vlasov-poisson system

1989 ◽  
Vol 189 (2) ◽  
pp. 265-317 ◽  
Author(s):  
John David Crawford ◽  
Peter D Hislop
Keyword(s):  
Poisson System ◽  
Spectral Deformation

scholarly journals Observers of Vlasov-Poisson system

2020 ◽  
Vol 53 (2) ◽  
pp. 5946-5951
Author(s):  
Amadou Cisse ◽  
Mohamed Boutayeb
Keyword(s):  
Poisson System

Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state

2019 ◽  
Vol 16 (01) ◽  
pp. 131-156
Author(s):  
Lanoir Addala ◽  
Mohamed Lazhar Tayeb
Keyword(s):  
Nonlinear Diffusion ◽  
Collision Operator ◽  
Nonlinear Diffusion Equation ◽  
One Dimension ◽  
Diffusion Limit ◽  
Poisson System ◽  
Nonlinear Relaxation ◽  
Contraction Property ◽  
Hilbert Expansion ◽  
Nonlinear Equilibrium

The diffusion approximation for a Boltzmann–Poisson system is studied. Nonlinear relaxation type collision operator is considered. A relative entropy is used to prove useful [Formula: see text]-estimates for the weak solutions of the scaled Boltzmann equation (coupled to Poisson) and to prove the convergence of the solution toward the solution of a nonlinear diffusion equation coupled to Poisson. In one dimension, a hybrid Hilbert expansion and the contraction property of the operator allow to exhibit a convergence rate.

Sign in / Sign up

Export Citation Format

Share Document