American Institute of Mathematical Sciences

Advanced
June  2009, 2(2): 345-362. doi: 10.3934/krm.2009.2.345

Milne problem for non-grey radiative transfer

J-F. Clouët 1, and  R. Sentis 1,

1. 

CEA, DAM-DIF, 91297 Arpajon Cedex, France, France

Received  November 2008 Revised  February 2009 Published  May 2009

We study the non-linear Milne problem for radiative transfer equation: after proving the existence of a brightness temperature, we propose and evaluate different formulas for evaluating it. Numerical tests show that as much as 20% difference between surface temperature and brightness temperature may be exhibited. An analytical expression for the out-coming flux is also given.
Keywords: Non-linear half space problem., Milne Problem, Chandrasekhar function.
Mathematics Subject Classification: Primary: 35Q99; Secondary: 35F3.
Citation: J-F. Clouët, R. Sentis. Milne problem for non-grey radiative transfer. Kinetic and Related Models, 2009, 2 (2) : 345-362. doi: 10.3934/krm.2009.2.345
[1]

Niclas Bernhoff. On half-space problems for the weakly non-linear discrete Boltzmann equation. Kinetic and Related Models, 2010, 3 (2) : 195-222. doi: 10.3934/krm.2010.3.195
[2]

Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424
[3]

Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. FLUID STRUCTURE INTERACTION PROBLEM WITH CHANGING THICKNESS NON-LINEAR BEAM Fluid structure interaction problem with changing thickness non-linear beam. Conference Publications, 2011, 2011 (Special) : 813-823. doi: 10.3934/proc.2011.2011.813
[4]

Vasily Denisov and Andrey Muravnik. On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations. Electronic Research Announcements, 2003, 9: 88-93.

[5]

Bei Hu, Lishang Jiang, Jin Liang, Wei Wei. A fully non-linear PDE problem from pricing CDS with counterparty risk. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 2001-2016. doi: 10.3934/dcdsb.2012.17.2001
[6]

Leif Arkeryd, Anne Nouri. A Milne problem from a Bose condensate with excitations. Kinetic and Related Models, 2013, 6 (4) : 671-686. doi: 10.3934/krm.2013.6.671
[7]

Linglong Du. Characteristic half space problem for the Broadwell model. Networks and Heterogeneous Media, 2014, 9 (1) : 97-110. doi: 10.3934/nhm.2014.9.97
[8]

Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096
[9]

Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557
[10]

Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the half-space. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957-982. doi: 10.3934/cpaa.2007.6.957
[11]

Chiu-Ya Lan, Huey-Er Lin, Shih-Hsien Yu. The Green's functions for the Broadwell Model in a half space problem. Networks and Heterogeneous Media, 2006, 1 (1) : 167-183. doi: 10.3934/nhm.2006.1.167
[12]

Ihsane Bikri, Ronald B. Guenther, Enrique A. Thomann. The Dirichlet to Neumann map - An application to the Stokes problem in half space. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 221-230. doi: 10.3934/dcdss.2010.3.221
[13]

Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems and Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169
[14]

Viorel Barbu, Gabriela Marinoschi. An identification problem for a linear evolution equation in a banach space. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1429-1440. doi: 10.3934/dcdss.2020081
[15]

Akhlad Iqbal, Praveen Kumar. Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems. Numerical Algebra, Control and Optimization, 2021  doi: 10.3934/naco.2021040
[16]

Kurt Falk, Marc Kesseböhmer, Tobias Henrik Oertel-Jäger, Jens D. M. Rademacher, Tony Samuel. Preface: Diffusion on fractals and non-linear dynamics. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : i-iv. doi: 10.3934/dcdss.201702i
[17]

Dmitry Dolgopyat. Bouncing balls in non-linear potentials. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 165-182. doi: 10.3934/dcds.2008.22.165
[18]

Dorin Ervin Dutkay and Palle E. T. Jorgensen. Wavelet constructions in non-linear dynamics. Electronic Research Announcements, 2005, 11: 21-33.

[19]

Armin Lechleiter. Explicit characterization of the support of non-linear inclusions. Inverse Problems and Imaging, 2011, 5 (3) : 675-694. doi: 10.3934/ipi.2011.5.675
[20]

Denis Serre. Non-linear electromagnetism and special relativity. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 435-454. doi: 10.3934/dcds.2009.23.435

2020 Impact Factor: 1.432

Tools

Metrics

  • PDF downloads (83)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy