STATIONARY WIGNER EQUATION WITH INFLOW BOUNDARY CONDITIONS: WILL A SYMMETRIC POTENTIAL YIELD A SYMMETRIC SOLUTION?
STATIONARY WIGNER EQUATION WITH INFLOW BOUNDARY CONDITIONS: WILL A SYMMETRIC POTENTIAL YIELD A SYMMETRIC SOLUTION?
复制标题
具有流入边界条件的稳态维格纳方程：对称势能产生对称解吗？
DOI：
10.1137/130941754
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发表时间：
2014-01-01
影响因子：
1.9
通讯作者：
Sun, Zhangpeng
中科院分区：
文献类型：
--
作者：
Li, Ruo;Lu, Tiao;Sun, Zhangpeng
基于文献[A. Arnold，H. Lange和P.F. Zweifel，J. Math. Phys.，41（2000），pp. 7167-7180]在没有任何附加先决条件的情况下，我们证明了具有流入边界条件的Wigner方程的解只有当势是对称的时才是对称的。这改进了[D.塔吉湖Genovese和F.罗西，欧罗巴。信件：74（2006），pp. 1060-1066]，这取决于在Neumann级数中制定的解决方案的收敛性。通过数值研究，我们给出了三种不同数值格式的对称剖面数值解的收敛性。这意味着迎风格式也能得到对称的数值解，与[D.塔吉湖Genovese和F.罗西，欧罗巴。信件：74（2006），pp. 1060-1066]。
Based on the well-posedness of the stationary Wigner equation with inflow boundary conditions given in [A. Arnold, H. Lange, and P. F. Zweifel, J. Math. Phys., 41 (2000), pp. 7167-7180] we prove without any additional prerequisite conditions that the solution of the Wigner equation with inflow boundary conditions will be symmetric only if the potential is symmetric. This improves the result in [D. Taj, L. Genovese, and F. Rossi, Europhys. Lett., 74 (2006), pp. 1060-1066], which depends on the convergence of the solution formulated in the Neumann series. By numerical studies, we present the convergence of the numerical solution to the symmetric profile for three different numerical schemes. This implies that the upwind schemes can also yield a symmetric numerical solution, contrary to the argument given in [D. Taj, L. Genovese, and F. Rossi, Europhys. Lett., 74 (2006), pp. 1060-1066].