, Volume 45, Issue 2, pp 197-208
Date: 31 Mar 2009

Unique solvability of the stationary Fokker-Planck equation in a class of positive functions

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Abstract

We study the stationary Focker-Planck equation Δu − div(u f) = 0 with a given vector field f of the class C 0 (R n ) on the basis of a fixed point principle that generalizes the contraction mapping method. Next, we introduce a parameter in the equation and prove the unique solvability of the equation Δu − div( f) = 0 with the parameter in the class of positive slowly increasing functions. We reveal the analytic dependence of the positive solution u on the parameter γ. Pointwise estimates for positive solutions are proved.

Original Russian Text © A.I. Noarov, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 2, pp. 191–202.