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Stationary Fokker–Planck equation on noncompact manifolds and in unbounded domains

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Abstract

We investigate the Fokker–Planck equation on an infinite cylindrical surface and in an infinite strip with reflecting boundary conditions, prove the existence of a positive (not necessarily integrable) solution, and derive various conditions on the vector field f that are sufficient for the existence of a solution that is the probability density. In particular, these conditions are satisfied for some vector fields f with integral trajectories going to infinity.

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Authors and Affiliations

  1. Institute of Numerical Mathematics, RAS, Moscow, Russia

    A. I. Noarov

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  1. A. I. Noarov
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Correspondence to A. I. Noarov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 189, No. 3, pp. 453–463, December, 2016.

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Noarov, A.I. Stationary Fokker–Planck equation on noncompact manifolds and in unbounded domains. Theor Math Phys 189, 1796–1805 (2016). https://doi.org/10.1134/S0040577916120114

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  • DOI: https://doi.org/10.1134/S0040577916120114

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