Existence Theory  for Rosseland Equation and Its Homogenized Equation

ZHANG Qiao-fu; CUI Jun-zhi

doi:10.3879/j.issn.1000-0887.2012.12.010

Volume 33 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2012 > 33(12): 1487-1502

ZHANG Qiao-fu, CUI Jun-zhi. Existence Theory for Rosseland Equation and Its Homogenized Equation[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1487-1502. doi: 10.3879/j.issn.1000-0887.2012.12.010

Citation:

PDF( 450 KB)

Existence Theory for Rosseland Equation and Its Homogenized Equation

doi: 10.3879/j.issn.1000-0887.2012.12.010

LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R.China

Received Date: 2011-12-01
Rev Recd Date: 2012-06-15
Publish Date: 2012-12-15

Abstract

Abstract

The global boundness and existence were presented for the kind of Rosseland equation with a general growth condition.A linearized map in a closed convex set was defined. The image set was precompact and this map was continuous, so there existed a fixed point. The Multiple-scale expansion method was used to obtain the homogenized equation.This equation satisfied a similar growth condition.
- nonlinear elliptic equation,
- fixed point,
- mixed boundary conditions,
- growth conditions,
- maximal regularity,
- homogenized equation

FullText(HTML)

References(16)

References

[1]	ZHANG Qiao-fu, CUI Jun-zhi.Multi-scale analysis method for combined conductionradiation heat transfer of periodic composites[C]//Advances in Heterogeneous Material Mechanics. Lancaster: DEStech Publications, 2011: 461-464.
[2]	Modest M F. Radiative Heat Transfer[M]. 2nd. San Diego: McGrawHill, 2003: 450-453.
[3]	Laitinen M T. Asymptotic analysis of conductiveradiative heat transfer[J]. Asymptotic Analysis, 2002, 29(3): 323-342.
[4]	Griepentrog J A, Recke L. Linear elliptic boundary value problems with non-smooth data: normal solvability on SobolevCampanato spaces[J]. Math Nachr, 2001, 225(1): 39-74.
[5]	ZHANG Qiao-fu. Divergence form nonlinear nonsmooth parabolic equations with locally arbitrary growth conditions and nonlinear maximal regularity. arXivPreprint[math.AP], 2012, arXiv:1205.3237v1.
[6]	Gröger K. A W1,p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations[J].Math Ann, 1989, 283(4): 679-687.
[7]	WU Zhuo-qun, YIN Jing-xue, WANG Chun-peng. Elliptic and Parabolic Equations[M].Singapore: World Scientific, 2006: 105-111.
[8]	Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order[M].Berlin: Springer, 2001: 171-280.
[9]	ZHANG Qiao-fu. Divergence form nonlinear nonsmooth elliptic equations with locally arbitrary growth conditions and nonlinear maximal regularity. arXivPreprint[math.AP], 2012, arXiv:1205.2412v1.
[10]	ZHANG Qiao-fu, CUI Jun-zhi. Regularity of the correctors and local gradient estimate of the homogenization for the elliptic equation: linear periodic case. arXivPreprint[math.AP], 2011, arXiv: 1109.1107v1.
[11]	Cioranescu D, Donato P. An Introduction to Homogenization[M].Oxford: Oxford University Press, 1999: 33-140.
[12]	Fusco N, Moscariello G. On the homogenization of quasilinear divergence structure operators[J].Annali di Matematica Pura ed Applicata, 1986, 146(1): 1-13.
[13]	Avellaneda M, Lin F H. Compactness method in the theory of homogenization[J].Comm Pure Appl Math, 1987, 40(6): 803-847.
[14]	Kenig C E, Lin F H, Shen Z W. Homogenization of elliptic systems with Neumann boundary conditions. arXivPreprint[math.AP], 2010, arXiv: 1010.6114v1.
[15]	HE Wen-ming, CUI Jun-zhi.Error estimate of the homogenization solution for elliptic problems with small periodic coefficients on L∞(Ω)[J]. Science China Mathematics, 2010, 53(5): 1231-1252.
[16]	HE Wen-ming, CUI Jun-zhi. A finite element method for elliptic problems with rapidly oscillating coefficients[J].BIT Numerical Mathematics, 2007, 47: 77-102.