Applied Mathematics and Mechanics

, Volume 33, Issue 12, pp 1595–1612 | Cite as

Existence theory for Rosseland equation and its homogenized equation

  • Qiao-fu Zhang (张乔夫)Email author
  • Jun-zhi Cui (崔俊芝)


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

nonlinear elliptic equation fixed point mixed boundary condition growth condition maximal regularity homogenized equation 

Chinese Library Classification


2010 Mathematics Subject Classification

35J66 35B27 


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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Qiao-fu Zhang (张乔夫)
    • 1
    Email author
  • Jun-zhi Cui (崔俊芝)
    • 1
  1. 1.State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingP. R. China

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