# Frontiers of Mathematics in China

 Front. Math. China    2017, Vol. 12 Issue (4) : 907-919     DOI: 10.1007/s11464-017-0612-9
 RESEARCH ARTICLE |
Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions
Ruo LI1,2, Tiao LU1,2,3(), Zhangpeng SUN1
1. School of Mathematical Sciences, Peking University, Beijing 100871, China
2. HEDPS & CAPT, LMAM, Peking University, Beijing 100871, China
3. Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
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 Abstract We study the stationary Wigner equation on a bounded, onedimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys., 2001, 30(4-6): 507–520]. The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even part and the odd part. Without using a cutoff approximation around zero velocity, we prove that the initial value problem for the even part is well-posed. For the odd part, we prove the uniqueness of the solution in the odd L2-space by analyzing the moment system. An example is provided to show that how to use the analysis to obtain the solution of the stationary Wigner equation with inflow boundary conditions. Corresponding Authors: Tiao LU Issue Date: 06 July 2017
 Cite this article: Ruo LI,Tiao LU,Zhangpeng SUN. Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions[J]. Front. Math. China, 2017, 12(4): 907-919. URL: http://journal.hep.com.cn/fmc/EN/10.1007/s11464-017-0612-9 http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/907
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