Calculating Steady States for a Fokker–Planck Equation
✍ Scribed by J. Guíñez; R. Quintero; A.D. Rueda
- Book ID
- 110292512
- Publisher
- Akadmiai Kiad
- Year
- 2001
- Tongue
- English
- Weight
- 236 KB
- Volume
- 91
- Category
- Article
- ISSN
- 1588-2632
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## Abstract In this paper we investigate the non‐linear Vlasov–Fokker–Planck (VFP) equation, a both physically and mathematically interesting modification of Vlasov's equation, which describes a plasma in a thermal bath. We prove existence, uniqueness and representation results for steady states of
The form of steady state solutions to the Vlasov᎐Poisson᎐Fokker᎐Planck system is known from the works of Dressler and others. In these papers an external < < potential is present which tends to infinity as x ª ϱ. It is shown here that this assumption is needed to obtain nontrivial steady states. Thi
A simple model of relaxation phenomena is defined with a variable strength of interaction, where the interaction term is given by a Gaussian unitary ensemble. A set of Fokker-Planck equations are derived which describe the gradual delocalization of the eigenstates with respect to the unperturbed ene