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
Access Full Article
topAbstract
topHow to cite
topAgoshkov, 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- V.A. Ambartsumyan, Scattering and absorption of light in planetary atmospheres. Uchen. Zap. TsAGI82 (1941), in Russian.
- S. Chandrasekhar, Radiative Transfer. New York (1960).
- J.-L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Paris (1968).
- 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.
- V.I. Agoshkov, Generalized solutions of transport equations and their smoothness properties. Nauka, Moscow (1988), in Russian.
- V.I. Agoshkov, Reflection operators and domain decomposition methods in transport theory problems. Sov. J. Numer. Anal. Math. Modelling2 (1987) 325-347.
- 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.
- V.S. Vladimirov, Mathematical problems of monenergetic particle transport theory. Trudy Mat. Inst. Steklov61 (1961), in Russian.
- G.I. Marchuk, Design of Nuclear Reactors. Atomizdat, Moscow (1961), in Russian.
- V.V. Sobolev, Light Scattering in Planetary Atmospheres. Pergamon Press, Oxford, U.K. (1973).
- G.I. Marchuk and V.I. Agoshkov, Reflection Operators and Contemporary Applications to Radiative Transfer. Appl. Math. Comput.80 (1995) 1-19.
- 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.
- 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).
- 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.
- Ill-posed problems in natural Sciences, edited by A.N. Tikhonov. Moscow, Russia - VSP, Netherlands (1992).
- A.L. Ivankov, Inverse problems for the nonstationary kinetic transport equation. In [15].
- A.I. Prilepko, D.G. Orlovskii and I.A. Vasin, Inverse problems in mathematical physics. In [15].
- Yu.E. Anikonov, New methods and results in multidimensional inverse problems for kinetic equations. In [15].
- E.C. Titchmarsh, Introduction to the Theory of Fourier Integral. New York (1937).
- C. Bardos, Mathematical approach for the inverse problem in radiative media (1986), not published.
- K.M. Case, Inverse problem in transport theory. Phys. Fluids16 (1973) 16-7-1611.
- 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).
- 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).
- N.J. McCormick, Recent Development in inverse scattering transport method. Trans. Theory Statist. Phys.13 (1984) 15-28.
- C. Bardos, R. Santos and R. Sentis, Diffusion approximation and the computation of critical size. Trans. Amer. Math. Soc.284 (1986) 617-649.
- C. Bardos, R. Caflish and B. Nicolaenko, Different aspect of the Milne problem. Trans. Theory Statist. Phys.16 (1987) 561-585.
- 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.
- V.I. Agoshkov and C. Bardos, Inverse radiative problems: The problem on boundary function. CMLA, ENS de Cachan, Preprint No. 9801 (1998).
- 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).
- V.I. Agoshkov and C. Bardos, Optimal control approach in 3D-inverse radiative problem on boundary function (to appear).
- 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).
- S.I. Kabanikhin and A.L. Karchevsky, Optimization methods of solving inverse problems of geoelectrics. In [15].
- F. Coron, F. Golse and C. Sulem, A Classification of Well-Posed Kinetic Layer Problems. Comm. Pure Appl. Math.41 (1988) 409-435.
- R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, CEA. Masson, Tome 9.
- R. Glowinski and J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numer. (1994) 269-378.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.