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Newtonian limit and trend to equilibrium for the relativistic Fokker-Planck equation. (English) Zbl 1288.82048
The Fokker-Plank equation is considered in the paper. The behavior of solutions to the relativistic Fokker-Planck equation for the case when the speed of light \(c \to \infty\) is studied. Under some additional assumptions on the initial data it is shown that its solutions converge in \(L^1\)-norm to solutions of the non-relativistic Fokker-Planck equation.
Another remarkable fact concerning the behavior of solutions to the relativistic Fokker-Planck equation is its exponential convergence as \(t \to \infty\) to the global thermodynamical equilibrium state in \(L^2\)-norm.
As a remark, the reviewer would like to suggest that the restriction \(\gamma >7\), \(w>9\) on the initial data is purely technical and apparently could be avoided.

MSC:
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
35Q84 Fokker-Planck equations
35Q75 PDEs in connection with relativity and gravitational theory
83A05 Special relativity
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