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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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