We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys....We study the stationary Wigner equation on a bounded, one- dimensional 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-spaee 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.展开更多
文摘We study the stationary Wigner equation on a bounded, one- dimensional 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-spaee 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.
