Geodesic
Quasi-steady-state particle distributions for an equation of the Landau–Fokker–Planck type with sources
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 2, pp. 307-317

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The formation of nonequilibrium particle distributions for the power-law interaction potentials $U=\alpha/r^\beta$, where $1\le\beta4$, is considered. The analytical and numerical studies are based on a one-dimensional (in the velocity space) kinetic equation of the Landau–Fokker–Planck type with energy (particle) sources (sinks) localized in the high-energy range. Fully conservative finite-difference schemes are used for numerical modeling. The resulting asymptotic estimates are confirmed by numerical computations. The results can be used to predict the behavior of intrinsic and extrinsic semiconductors influenced by particle fluxes or electromagnetic radiation. 
@article{ZVMMF_2006_46_2_a10,
     author = {V. I. Karas' and I. F. Potapenko},
     title = {Quasi-steady-state particle distributions for an equation of the {Landau{\textendash}Fokker{\textendash}Planck} type with sources},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {307--317},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_2_a10/}
}
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V. I. Karas'; I. F. Potapenko. Quasi-steady-state particle distributions for an equation of the Landau–Fokker–Planck type with sources. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 2, pp. 307-317. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_2_a10/