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

• Articles • Previous Articles    

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)

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

2010 MSC Number: 

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