Kinetic Equation for Quantum Fermi Gases and the Analytic Solution of Boundary Value Problems

被引：0
作者：
A. V. Latyshev
A. A. Yushkanov
机构：
[1] Moscow Pedagogical University,
来源：
Theoretical and Mathematical Physics | 2003年 / 134卷
关键词：
boundary value problem; kinetic equation; dilute Fermi gas; distribution function; generalized Smoluchowski problem; temperature jumps; concentration jumps; chemical potential jumps;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We construct a kinetic equation describing the behavior of quantum Fermi gases with the molecule collision frequency proportional to the molecule velocity. We obtain an analytic solution of the generalized Smoluchowski problem with the temperature gradient and the mass flow velocity specified away from the surface. We find exact formulas for jumps of the gas temperature, concentration, and chemical potential. Analysis of limit cases demonstrates a transition of the quantum Fermi gas to the classical or degenerate gas.
引用
收藏
页码：271 / 284
页数：13
相关论文
共 50 条
  • [41] THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT
    莫嘉淇
    林万涛
    王辉
    Annals of Differential Equations, 2003, (04) : 521 - 526
  • [42] On boundary value problems for a discrete generalized Emden-Fowler equation
    Yu, Jianshe
    Guo, Zhiming
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 231 (01) : 18 - 31
  • [43] BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATION IN SPECIAL BANACH SPACE
    Moustafa, Beddani
    Benaouda, Hedia
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2021, 19 (02): : 239 - 251
  • [44] Boundary value problems of discrete generalized Emden-Fowler equation
    Jianshe Yu
    Zhiming Guo
    Science in China Series A: Mathematics, 2006, 49 : 1303 - 1314
  • [45] UNIQUENESS OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS FOR THE BIHARMONIC EQUATION IN A BALL
    Karachik, Valery V.
    Sadybekov, Makhmud A.
    Torebek, Berikbol T.
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
  • [46] Symmetries, invariances, and boundary value problems for the Hamilton-Jacobi equation
    Goldstein, GR
    Goldstein, JA
    Soeharyadi, Y
    JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2006, 8 (03) : 205 - 222
  • [47] Positive solutions of fractional differential equation nonlocal boundary value problems
    Tan, Jingjing
    Cheng, Caozong
    Zhang, Xinguang
    ADVANCES IN DIFFERENCE EQUATIONS, 2015,
  • [48] On the solvability of the boundary value problems for the elliptic equation of high order on a plane
    Koshanov, B. D.
    Soldatov, A. P.
    BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018, 91 (03): : 24 - 30
  • [49] Boundary value problems of discrete generalized Emden-Fowler equation
    Yu Jianshe
    Guo Zhiming
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (10): : 1303 - 1314
  • [50] Eigenvalue comparisons for a class of boundary value problems of discrete beam equation
    Ji, Jun
    Yang, Bo
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (09) : 5402 - 5408
12345