Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures

Bogachev VI, Röckner M, Shaposhnikov SV (2019)
JOURNAL OF FUNCTIONAL ANALYSIS 276(12): 3681-3713.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
We study convergence in variation of probability solutions of nonlinear Fokker-Planck-Kolrnogorov equations to stationary solutions. We obtain sufficient conditions for the exponential convergence of solutions to the stationary solution in case of coefficients that can have an arbitrary growth at infinity and depend on the solutions through convolutions with unbounded discontinuous kernels. In addition, we study a more difficult case where the nonlinear equation has several stationary solutions and convergence to a stationary solution depends on initial data. Finally, we obtain sufficient conditions for solvability of nonlinear Fokker-Planck-Kolmogorov equations. (C) 2019 Elsevier Inc. All rights reserved.
Stichworte
Nonlinear; Fokker-Planck-Kolrnogorov equation; Stationary measure; Exponential convergence
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL OF FUNCTIONAL ANALYSIS
Band
276
Ausgabe
12
Seite(n)
3681-3713
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2935865

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Bogachev VI, Röckner M, Shaposhnikov SV. Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures. JOURNAL OF FUNCTIONAL ANALYSIS. 2019;276(12):3681-3713.
Bogachev, V. I., Röckner, M., & Shaposhnikov, S. V. (2019). Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures. JOURNAL OF FUNCTIONAL ANALYSIS, 276(12), 3681-3713. doi:10.1016/j.jfa.2019.03.014
Bogachev, V. I., Röckner, M., and Shaposhnikov, S. V. (2019). Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures. JOURNAL OF FUNCTIONAL ANALYSIS 276, 3681-3713.
Bogachev, V.I., Röckner, M., & Shaposhnikov, S.V., 2019. Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures. JOURNAL OF FUNCTIONAL ANALYSIS, 276(12), p 3681-3713.
V.I. Bogachev, M. Röckner, and S.V. Shaposhnikov, “Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures”, JOURNAL OF FUNCTIONAL ANALYSIS, vol. 276, 2019, pp. 3681-3713.
Bogachev, V.I., Röckner, M., Shaposhnikov, S.V.: Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures. JOURNAL OF FUNCTIONAL ANALYSIS. 276, 3681-3713 (2019).
Bogachev, Vladimir I., Röckner, Michael, and Shaposhnikov, Stanislav V. “Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures”. JOURNAL OF FUNCTIONAL ANALYSIS 276.12 (2019): 3681-3713.