Differential Equations

, Volume 45, Issue 2, pp 197–208 | Cite as

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

  • A. I. Noarov
Partial Differential Equations

Abstract

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(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.

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • A. I. Noarov
    • 1
  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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