The Fokker-Planck Equation with Absorbing Boundary Conditions in Bounded Domains
The Fokker-Planck Equation with Absorbing Boundary Conditions in Bounded Domains
复制标题
有界域中具有吸收边界条件的福克-普朗克方程
DOI：
10.1137/16m1109928
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Jaewoo Jung
中科院分区：
文献类型：
--
作者：
H. Hwang;J. Jang;Jaewoo Jung
本文研究了多维有界域中具有吸收边界条件的 Fokker-Planck 方程的初边值问题。首先，我们通过构造正则化方程的解并通过均匀的 $L^{1}$ 和 $L^{\infty }$ 估计传递到极限来建立适定性理论。其次，对于具有平滑边界的一般多维域，我们证明了解在远离奇异集的地方是平滑的，并且局部保持连续直到奇异集。
In this paper, we study the initial-boundary value problem of the Fokker--Planck equation with absorbing boundary conditions in multidimensional bounded domains. First, we establish a well-posedness theory by constructing a solution for the regularized equation and passing to the limit by uniform $L^{1}$ and $L^{\infty }$ estimates. Second, for a general multidimensional domain with a smooth boundary, we show that the solution is smooth far from the singular set and locally Holder continuous up to the singular set.