Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (12): 1595-1612.doi: https://doi.org/10.1007/s10483-012-1646-6

• 论文 • 上一篇    

Existence theory for Rosseland equation and its homogenized equation

张乔夫, 崔俊芝   

  1. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China
  • 收稿日期:2011-12-01 修回日期:2012-06-15 出版日期:2012-12-10 发布日期:2012-12-10
  • 通讯作者: Qiao-fu ZHANG, Ph.D., E-mail: zhangqf@lsec.cc.ac.cn E-mail:zhangqf@lsec.cc.ac.cn
  • 基金资助:

    Supported by the National Basic Research Program of China (973 Program) (No. 2012CB025904) and the National Natural Science Foundation of China (No. 90916027)

Existence theory for Rosseland equation and its homogenized equation

Qiao-fu ZHANG, Jun-zhi CUI   

  1. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China
  • Received:2011-12-01 Revised:2012-06-15 Online:2012-12-10 Published:2012-12-10
  • Supported by:

    Supported by the National Basic Research Program of China (973 Program) (No. 2012CB025904) and the National Natural Science Foundation of China (No. 90916027)

摘要: The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

关键词: hyperbolic quaternion numbers, Lagrangian functions, generalized inertia forces

Abstract: The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

Key words: hyperbolic quaternion numbers, Lagrangian functions, generalized inertia forces

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