Unique solvability of the stationary Fokker-Planck equation in a class of positive functions
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- Noarov, A.I. Diff Equat (2009) 45: 197. doi:10.1134/S0012266109020062
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We study the stationary Focker-Planck equation Δu − div(uf) = 0 with a given vector field f of the class C0∞ (Rn) 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(uγf) = 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.