Optimal control approach in inverse radiative transfer problems: the problem on boundary function

Valeri I. Agoshkov; Claude Bardos

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 259-278
  • ISSN: 1292-8119

Abstract

top
The paper presents some results related to the optimal control approachs applying to inverse radiative transfer problems, to the theory of reflection operators, to the solvability of the inverse problems on boundary function and to algorithms for solution of these problems.

How to cite

top

Agoshkov, Valeri I., and Bardos, Claude. "Optimal control approach in inverse radiative transfer problems: the problem on boundary function." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 259-278. <http://eudml.org/doc/116563>.

@article{Agoshkov2010,
abstract = { The paper presents some results related to the optimal control approachs applying to inverse radiative transfer problems, to the theory of reflection operators, to the solvability of the inverse problems on boundary function and to algorithms for solution of these problems. },
author = {Agoshkov, Valeri I., Bardos, Claude},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; inverse problem; inverse radiative transfer problem; reflection operator; control equation operator; regularization parameter; iterative algorithm.; reflection operator; iterative algorithm; optimal control; inverse radiative transfer},
language = {eng},
month = {3},
pages = {259-278},
publisher = {EDP Sciences},
title = {Optimal control approach in inverse radiative transfer problems: the problem on boundary function},
url = {http://eudml.org/doc/116563},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Agoshkov, Valeri I.
AU - Bardos, Claude
TI - Optimal control approach in inverse radiative transfer problems: the problem on boundary function
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 259
EP - 278
AB - The paper presents some results related to the optimal control approachs applying to inverse radiative transfer problems, to the theory of reflection operators, to the solvability of the inverse problems on boundary function and to algorithms for solution of these problems.
LA - eng
KW - Optimal control; inverse problem; inverse radiative transfer problem; reflection operator; control equation operator; regularization parameter; iterative algorithm.; reflection operator; iterative algorithm; optimal control; inverse radiative transfer
UR - http://eudml.org/doc/116563
ER -

References

top
  1. V.A. Ambartsumyan, Scattering and absorption of light in planetary atmospheres. Uchen. Zap. TsAGI82 (1941), in Russian.  
  2. S. Chandrasekhar, Radiative Transfer. New York (1960).  
  3. J.-L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Paris (1968).  Zbl0179.41801
  4. V.I. Lebedev and V.I. Agoshkov, The Poincaré-Steklov Operators and their Applications in Analysis. Dept. of Numerical Math. of the USSR Academy of Sciences, Moscow (1983), in Russian.  Zbl0547.47029
  5. V.I. Agoshkov, Generalized solutions of transport equations and their smoothness properties. Nauka, Moscow (1988), in Russian.  Zbl0664.35070
  6. V.I. Agoshkov, Reflection operators and domain decomposition methods in transport theory problems. Sov. J. Numer. Anal. Math. Modelling2 (1987) 325-347.  Zbl0825.65110
  7. V.I. Agoshkov, On the existence of traces of functions in spaces used in transport theory problems. Dokl. Akad. Nauk SSSR288 (1986) 265-269, in Russian.  Zbl0636.46038
  8. V.S. Vladimirov, Mathematical problems of monenergetic particle transport theory. Trudy Mat. Inst. Steklov61 (1961), in Russian.  
  9. G.I. Marchuk, Design of Nuclear Reactors. Atomizdat, Moscow (1961), in Russian.  
  10. V.V. Sobolev, Light Scattering in Planetary Atmospheres. Pergamon Press, Oxford, U.K. (1973).  
  11. G.I. Marchuk and V.I. Agoshkov, Reflection Operators and Contemporary Applications to Radiative Transfer. Appl. Math. Comput.80 (1995) 1-19.  Zbl0831.65146
  12. V.I. Agoshkov, Domain decomposition methods in problems of hydrodynamics. I. Problem plain circulation in ocean. Moscow: Department of Numerical Mathematics, Preprint No. 96 (1985) 12, in Russian.  
  13. V.I. Agoshkov, Domain decomposition methods and perturbation methods for solving some time dependent problems of fluid dynamics, in Proc. of First International Interdisciplinary Conference. Olympia -91 (1991).  
  14. V.I. Agoshkov, Control theory approaches in: data assimilation processes, inverse problems, and hydrodynamics. Computer Mathematics and its Applications, HMS/CMA 1 (1994) 21-39.  Zbl0858.65100
  15. Ill-posed problems in natural Sciences, edited by A.N. Tikhonov. Moscow, Russia - VSP, Netherlands (1992).  
  16. A.L. Ivankov, Inverse problems for the nonstationary kinetic transport equation. In [15].  Zbl0785.45007
  17. A.I. Prilepko, D.G. Orlovskii and I.A. Vasin, Inverse problems in mathematical physics. In [15].  
  18. Yu.E. Anikonov, New methods and results in multidimensional inverse problems for kinetic equations. In [15].  Zbl0786.35137
  19. E.C. Titchmarsh, Introduction to the Theory of Fourier Integral. New York (1937).  Zbl0017.40404
  20. C. Bardos, Mathematical approach for the inverse problem in radiative media (1986), not published.  
  21. K.M. Case, Inverse problem in transport theory. Phys. Fluids16 (1973) 16-7-1611.  
  22. L.P. Niznik and V.G. Tarasov, Reverse scattering problem for a transport equation with respect to directions. Preprint, Institute of Mathematics, Academy Sciences of the Ukrainian SSR (1980).  
  23. K.K. Hunt and N.J. McCormick, Numerical test of an inverse method for estimating single-scattering parameters from pulsed multiple-scattering experiments. J. Opt. Soc. Amer. A.2 (1985).  
  24. N.J. McCormick, Recent Development in inverse scattering transport method. Trans. Theory Statist. Phys.13 (1984) 15-28.  
  25. C. Bardos, R. Santos and R. Sentis, Diffusion approximation and the computation of critical size. Trans. Amer. Math. Soc.284 (1986) 617-649.  Zbl0508.60067
  26. C. Bardos, R. Caflish and B. Nicolaenko, Different aspect of the Milne problem. Trans. Theory Statist. Phys.16 (1987) 561-585.  Zbl0643.35089
  27. V.P. Shutyaev, Integral reflection operators and solvability of inverse transport problem, in Integral equations in applied modelling. Kiev: Inst. of Electrodynamics, Academy of Sciences of Ukraine, Vol. 2 (1986) 243-244, in Russian.  
  28. V.I. Agoshkov and C. Bardos, Inverse radiative problems: The problem on boundary function. CMLA, ENS de Cachan, Preprint No. 9801 (1998).  Zbl0957.49018
  29. V.I. Agoshkov and C. Bardos, Inverse radiative problems: The problem on the right-hand-side function. CMLA, ENS de Cachan, Preprint No. 9802 (1998).  
  30. V.I. Agoshkov and C. Bardos, Optimal control approach in 3D-inverse radiative problem on boundary function (to appear).  Zbl0957.49018
  31. V.I. Agoshkov, C. Bardos, E.I. Parmuzin and V.P. Shutyaev, Numerical analysis of iterative algorithms for an inverse boundary transport problem (to appear).  Zbl1010.82035
  32. S.I. Kabanikhin and A.L. Karchevsky, Optimization methods of solving inverse problems of geoelectrics. In [15].  Zbl0833.65107
  33. F. Coron, F. Golse and C. Sulem, A Classification of Well-Posed Kinetic Layer Problems. Comm. Pure Appl. Math.41 (1988) 409-435.  Zbl0632.76088
  34. R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, CEA. Masson, Tome 9.  Zbl0642.35001
  35. R. Glowinski and J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numer. (1994) 269-378.  Zbl0838.93013

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.