@article{COCV_2000__5__259_0, author = {Agoshkov, Valeri I. and Bardos, Claude}, title = {Optimal control approach in inverse radiative transfer problems : the problem on boundary function}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {259--278}, publisher = {EDP-Sciences}, volume = {5}, year = {2000}, mrnumber = {1765426}, zbl = {0957.49018}, language = {en}, url = {http://archive.numdam.org/item/COCV_2000__5__259_0/} }

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 PY - 2000 SP - 259 EP - 278 VL - 5 PB - EDP-Sciences UR - http://archive.numdam.org/item/COCV_2000__5__259_0/ LA - en ID - COCV_2000__5__259_0 ER -

%0 Journal Article %A Agoshkov, Valeri I. %A Bardos, Claude %T Optimal control approach in inverse radiative transfer problems : the problem on boundary function %J ESAIM: Control, Optimisation and Calculus of Variations %D 2000 %P 259-278 %V 5 %I EDP-Sciences %U http://archive.numdam.org/item/COCV_2000__5__259_0/ %G en %F COCV_2000__5__259_0

Agoshkov, Valeri I.; Bardos, Claude. Optimal control approach in inverse radiative transfer problems : the problem on boundary function. ESAIM: Control, Optimisation and Calculus of Variations, Volume 5 (2000), pp. 259-278. http://archive.numdam.org/item/COCV_2000__5__259_0/

[1] Scattering and absorption of light in planetary atmospheres. Uchen. Zap. TsAGI 82 ( 1941), in Russian.

,[2] Radiative Transfer. New York ( 1960). | MR | Zbl

,[3] Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Paris ( 1968). | MR | Zbl

,[4] The Poincaré-Steklov Operators and their Applications in Analysis. Dept. of Numerical Math. of the USSR Academy of Sciences, Moscow ( 1983), in Russian. | MR | Zbl

and ,[5] Generalized solutions of transport equations and their smoothness properties. Nauka, Moscow ( 1988), in Russian. | MR

,[6] Reflection operators and domain decomposition methods in transport theory problems. Sov. J. Numer. Anal. Math. Modelling 2 ( 1987) 325-347. | MR | Zbl

,[7] On the existence of traces of functions in spaces used in transport theory problems. Dokl. Akad. Nauk SSSR 288 ( 1986) 265-269, in Russian. | MR | Zbl

,[8] Mathematical problems of monenergetic particle transport theory. Trudy Mat. Inst. Steklov 61 ( 1961), in Russian. | MR

,[9] Design of Nuclear Reactors. Atomizdat, Moscow ( 1961), in Russian.

,[10] Light Scattering in Planetary Atmospheres. Pergamon Press, Oxford, U.K. ( 1973).

,[11] Reflection Operators and Contemporary Applications to Radiative Transfer. Appl. Math. Comput. 80 ( 1995) 1-19. | MR | Zbl

and ,[12] 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. | MR | Zbl

,[13] 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). | Zbl

,[14] Control theory approaches in: data assimilation processes, inverse problems, and hydrodynamics. Computer Mathematics and its Applications, HMS/CMA 1 ( 1994) 21-39. | MR | Zbl

,[15] Ill-posed problems in natural Sciences, edited by A.N. Tikhonov. Moscow, Russia - VSP, Netherlands ( 1992). | MR

[16] Inverse problems for the nonstationary kinetic transport equation. In [15]. | Zbl

,[17] Inverse problems in mathematical physics. In [15]. | Zbl

, and ,[18] New methods and results in multidimensional inverse problems for kinetic equations. In [15]. | Zbl

,[19] Introduction to the Theory of Fourier Integral. New York ( 1937). | JFM

,[20] Mathematical approachfor the inverse problem in radiative media ( 1986), not published.

,[21] Inverse problem in transport theory. Phys. Fluids 16 ( 1973) 16-7-1611. | MR

,[22] Reverse scattering problem for a transport equation with respect to directions.Preprint, Institute of Mathematics, Academy Sciences of the Ukrainian SSR ( 1980). | MR

and ,[23] Numerical test of an inverse method for estimating single-scattering parameters from pulsed multiple-scattering experiments. J. Opt. Soc. Amer. A. 2 ( 1985).

and ,[24] Recent Development in inverse scattering transport method. Trans. Theory Statist. Phys. 13 ( 1984) 15-28. | MR

,[25] Diffusion approximation and the computation of critical size. Trans. Amer. Math. Soc. 284 ( 1986) 617-649. | MR | Zbl

, and ,[26] Different aspect of the Milne problem. Trans. Theory Statist. Phys. 16 ( 1987) 561-585. | MR | Zbl

, and ,[27] Integral renection 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] Inverse radiative problems: The problem on boundary function. CMLA, ENS de Cachan, Preprint No. 9801 ( 1998).

and ,[29] Inverse radiative problems: The problem on the right-hand-side function. CMLA, ENS de Cachan, Preprint No. 9802 ( 1998).

and ,[30] Optimal control approach in 3D-inverse radiative problem on boundary function (to appear).

and ,[31] Numerical analysis of iterative algorithms for an inverse boundary transport problem (to appear). | MR | Zbl

, , and ,[32] Optimization methods of solving inverse problems of geoelectric, In [15]. | Zbl

and ,[33] A Classification of Well-Posed Kinetic Layer Problems. Comm. Pure Appl. Math. 41 ( 1988) 409-435. | MR | Zbl

, and ,[34] Analyse mathématique et calcul numérique pour les sciences et les techniques, CEA. Masson, Tome 9. | Zbl

and ,[35] Exact and approximate controllability for distributed parameter systems. Acta Numer. ( 1994) 269-378. | MR | Zbl

and ,