数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1225-1232.doi: 10.1016/S0252-9602(09)60099-0

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DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS

 陈泽乾   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences P.O.Box 71010, 30 West District, Xiao-Hong Mountain, Wuhan 430071, China
  • 收稿日期:2007-05-28 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:

    Supported partially by the National Natural Science Foundation of China  (10775175)

DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS

 CHEN Ze-Qan   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences P.O.Box 71010, 30 West District, Xiao-Hong Mountain, Wuhan 430071, China
  • Received:2007-05-28 Online:2009-09-20 Published:2009-09-20
  • Supported by:

    Supported partially by the National Natural Science Foundation of China  (10775175)

摘要:

In this article, we are concerned with the Dirichlet problem of the stationary von Neumann--Landau wave equation: { ( -Δx + Δy ) Φ (x, y) = 0,     x, y ∈ Ω
   Φ | ∂Ω×∂Ω = f,
where Ω is a bounded domain in Rn. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

关键词: von Neumann Landau equation, wave functions, Dirichlet problem

Abstract:

In this article, we are concerned with the Dirichlet problem of the stationary von Neumann--Landau wave equation: { ( -Δx + Δy ) Φ (x, y) = 0,     x, y ∈ Ω
   Φ | ∂Ω×∂Ω = f,
where Ω is a bounded domain in Rn. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

Key words: von Neumann Landau equation, wave functions, Dirichlet problem

中图分类号: 

  • 35Q40