Convergence in variation of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary measures |
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Authors: | Vladimir I Bogachev Michael Röckner Stanislav V Shaposhnikov |
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Institution: | 1. Lomonosov Moscow State University, Russian Federation;2. National Research University Higher School of Economics, Russian Federation;3. Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany |
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Abstract: | We study convergence in variation of probability solutions of nonlinear Fokker–Planck–Kolmogorov 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. |
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Keywords: | 60J75 47G20 60G52 Nonlinear Fokker–Planck–Kolmogorov equation Stationary measure Exponential convergence |
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