论文标题
（非线性）Fokker-Planck-Kolmogorov方程的流量选择
Flow selections for (nonlinear) Fokker-Planck-Kolmogorov equations
论文作者
论文摘要
我们提供了一种方法，以选择线性和非线性fokker-planck-planck-kolmogorov方程（FPK方程）的解决方案流量，以实现欧几里得空间的度量。在线性情况下，我们的方法改善了作者先前工作的相似结果。我们对非线性方程式的流量选择的考虑，包括Nemytskii-Type系数特别有趣的情况，似乎是新的。我们还通过这种（受限制）流的唯一性来表征FPK方程的（受限制的）良好性。此外，我们表明，在线性案例中，这种流量是马尔可夫人，即它们满足Chapman-Kolmogorov方程。
We provide a method to select flows of solutions to the Cauchy problem for linear and nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) for measures on Euclidean space. In the linear case, our method improves similar results of a previous work of the author. Our consideration of flow selections for nonlinear equations, including the particularly interesting case of Nemytskii-type coefficients, seems to be new. We also characterize the (restricted) well-posedness of FPK equations by the uniqueness of such (restricted) flows. Moreover, we show that under suitable assumptions in the linear case such flows are Markovian, i.e. they fulfill the Chapman-Kolmogorov equations.
