The Fokker–Planck–Kolmogorov equation with nonlinear terms of local and nonlocal type

Bogachev, V.; Salakhov, D.; Shaposhnikov, S.

doi:10.1090/spmj/1826

The Fokker–Planck–Kolmogorov equation with nonlinear terms of local and nonlocal type
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by V. I. Bogachev, D. I. Salakhov and S. V. Shaposhnikov;
Translated by: V. I. Bogachev

St. Petersburg Math. J. 35 (2024), 749-767

DOI: https://doi.org/10.1090/spmj/1826

Published electronically: December 3, 2024

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Abstract:

Nonlinear Fokker–Planck–Kolmogorov equations are investigated. Sufficient conditions are obtained for the existence and uniqueness of a nonnegative solution with a prescribed value of the integral. Convergence of solutions for the Cauchy problem to a solution of the stationary equation is shown. An important distinction from the known results is a very general form of the nonlinearity, which makes it possible to consider simultaneously a local and nonlocal dependence of coefficients on solutions.

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St. Petersburg Mathematical Journal

The Fokker–Planck–Kolmogorov equation with nonlinear terms of local and nonlocal type
HTML articles powered by AMS MathViewer

Abstract: