RESEARCH ARTICLE

Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions

  • Ruo LI 1,2 ,
  • Tiao LU , 1,2,3 ,
  • Zhangpeng SUN 1
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  • 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

Received date: 04 May 2016

Accepted date: 03 Nov 2016

Published date: 06 Jul 2017

Copyright

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Ruo LI , Tiao LU , Zhangpeng SUN . Parity-decomposition and moment analysis for stationary Wigner equation with inflow boundary conditions[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 907 -919 . DOI: 10.1007/s11464-017-0612-9

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