Convergence in variation of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary measures
Convergence in variation of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary measures
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DOI：
10.1016/j.jfa.2019.03.014
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发表时间：
2018-01
影响因子：
1.7
通讯作者：
V. Bogachev;M. Rockner;S. V. Shaposhnikov
中科院分区：
文献类型：
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作者：
V. Bogachev;M. Rockner;S. V. Shaposhnikov
研究了非线性Fokker-Planck-Kolmogorov方程的概率解向平稳解变化的收敛性。我们得到了平稳解的指数收敛的充分条件，当系数可以在无穷远处任意增长并且依赖于通过无界不连续核卷积的解时。此外，我们研究了一个更困难的情况，其中非线性方程有多个平稳解，并且收敛到一个平稳解依赖于初始数据。最后，我们得到了非线性Fokker-Planck-Kolmogorov方程可解的充分条件。
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.