@article{TSP_2009_27_27_a2,
author = {A. S. Demidov and A. S. Kochurov and A. Yu. Popov},
title = {To the problem of the recovery of nonlinearities in equations of mathematical physics},
journal = {Trudy Seminara im. I.G. Petrovskogo},
pages = {74--123},
year = {2009},
volume = {27},
number = {27},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TSP_2009_27_27_a2/}
}
TY - JOUR AU - A. S. Demidov AU - A. S. Kochurov AU - A. Yu. Popov TI - To the problem of the recovery of nonlinearities in equations of mathematical physics JO - Trudy Seminara im. I.G. Petrovskogo PY - 2009 SP - 74 EP - 123 VL - 27 IS - 27 UR - http://geodesic.mathdoc.fr/item/TSP_2009_27_27_a2/ LA - ru ID - TSP_2009_27_27_a2 ER -
%0 Journal Article %A A. S. Demidov %A A. S. Kochurov %A A. Yu. Popov %T To the problem of the recovery of nonlinearities in equations of mathematical physics %J Trudy Seminara im. I.G. Petrovskogo %D 2009 %P 74-123 %V 27 %N 27 %U http://geodesic.mathdoc.fr/item/TSP_2009_27_27_a2/ %G ru %F TSP_2009_27_27_a2
A. S. Demidov; A. S. Kochurov; A. Yu. Popov. To the problem of the recovery of nonlinearities in equations of mathematical physics. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 27 (2009) no. 27, pp. 74-123. http://geodesic.mathdoc.fr/item/TSP_2009_27_27_a2/
[1] Andreev V. K., Kaptsov O. V., Pukhnachev V. V., Rodionov A. A., Primenenie teoretiko-gruppovykh metodov v gidrodinamike, Nauka, Novosibirsk, 1994 | MR
[2] Bezrodnykh S. I., Vlasov V. I., Demidov A. S., “Obratnaya zadacha dlya uravneniya Greda–Shafranova”, Materialy konferentsii, Mezhdunar. konf. “Sovremennye problemy matematiki, mekhaniki i ikh prilozhenie”, posvyaschennaya 70-letiyu rektora MGU akademika V. A. Sadovnichego (Moskva, 30 marta — 2 aprelya 2009 g.), MGU, M., 2009, 132
[3] Valiev A. D., Demidov A. S., “O neotritsatelnykh trigonometricheskikh polinomakh s fiksirovannym srednim, prokhodyaschikh cherez zadannye tochki”, Mat. zametki, 62:3 (1997), 468–471 | DOI | MR | Zbl
[4] Demidov A. S., “Ob obratnoi zadache dlya uravneniya Greda–Shafranova s affinnoi pravoi chastyu”, UMN, 55:6 (2000), 131–132 | DOI | MR | Zbl
[5] Demidov A. S., “O rekonstruktsii polinomialnykh nelineinostei v uravneniyakh matematicheskoi fiziki”, Int. Conf. “Diff. Equations Related Topics” dedicated to I. G. Petrovskii. Book of Abstracts, Moscow, 2007, 73–74
[6] Demidov A. S., Zakharov L. E., “Pryamaya i obratnaya zadachi v teorii ravnovesiya plazmy”, UMN, 29:6 (1974), 203 | MR
[7] Dubinskii Yu. A., “Nelineinye ellipticheskie i parabolicheskie uravneniya”, Sovrem. probl. matematiki, Itogi nauki i tekhniki, 9, VINITI, 1976, 5–130
[8] Zverev I. N., Smirnov N. N., Gazodinamika goreniya, Izd-vo Mosk. un-ta, M., 1987 | Zbl
[9] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-Entropiya i $\varepsilon$-emkost mnozhestv v funktsionalnykh prostranstvakh”, UMN, 14:2 (1959), 3–86 | MR | Zbl
[10] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1962 | MR
[11] Lyuk Yu., Spetsialnye matematicheskie funktsii i ikh approksimatsii, Mir, M., 1980
[12] Polia G., Sege G., Zadachi i teoremy iz analiza, GITTL, M., 1956
[13] Polyanin A. D., Zaitsev V. F., Spravochnik po nelineinym uravneniyam matematicheskoi fiziki: tochnye resheniya, Fizmatlit, M., 2002 | MR
[14] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, Izd-vo Mosk. un-ta, M., 1976 | MR
[15] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR
[16] Beretta E., Vogelius M., “An inverse problem originating from magnetohydrodynamics”, Arch. Rational Mech. Anal., 115 (1991), 137–152 | DOI | MR | Zbl
[17] Beretta E., Vogelius M., “An inverse problem originating from magnetohydrodynamics. II. The case of the Grad–Shafranov equation”, Indiana Univ. Math. J., 41 (1992), 1081–1118 | DOI | MR | Zbl
[18] Beretta E., Vogelius M., “An inverse problem originating from magnetohydrodynamics. III. Domains with corners of arbitrary angles”, Asymptotic Anal., 11 (1995), 289–315 | MR | Zbl
[19] Blum J., Buvat H., “An inverse problem in plasma physics: The identification of the current density profile in a tokamak”, Large-Scale Optimisation with Applications, Pt. I. Optimization in Inverse Problems and Design, eds. L. T. Biegler, T. F. Coleman, A. R. Conn, F. N. Santosa, Springer, New York, 2002 www.inria.fr/rapportsactivite/RA2002/idopt/bibliographie.html | MR
[20] Demidov A. S., “Sur la perturbation “singulière” dans un problème à frontière libre”, Proc. Conf. “Singular Perturbations and Boundary Layer Theory” (held in Lyon, 1976), Lect. Notes Math., 594, Springer, Berlin, 1977, 123–130 | DOI | MR
[21] Demidov A. S., Moussaoui M., “An inverse problem originating from magnetohydrodynamics”, Inverse Problems, 20 (2004), 137–154 | DOI | MR | Zbl
[22] Demidov A. S., Petrova V. V., Silantiev V. M., “On inverse and direct free boundary problems in the theory of plasma equilibrium in a Tokamak”, C. R. Acad. Sci. Paris. Sér. I, 323 (1996), 353–358 | MR | Zbl
[23] Pokhozhaev S. I., Handbook of Differential Equations: Stationary Partial Differential Equations, v. 5, ed. M. Chipot, Elsevier, Amsterdam, 2008, 49–209
[24] Pustovitov V. D., “Magnetic diagnostics: General principles and the problem of reconstruction of plasma current and pressure profiles in toroidal systems”, Nuclear Fusion, 41:6 (2001), 721–730 | DOI
[25] Pustovitov V. D., “Theoretical principles of the plasma-equilibrium control in stellarators”, Rev. Plasma Phys., 21 (2001), 1–201 | DOI
[26] Suzuki Y., Yamada H., Nakajima N., Watanabe K., Nakamura Y., Hayashi T., “Theoretical considerations of doublet-like configuration in LHD”, Nuclear Fusion, 46 (2006), 123–132 | DOI
[27] Vogelius M., “An inverse problem for the equation $\Delta u = -cu -d$”, Ann. Inst. Fourier, 44 (1994), 1181–1209 | DOI | MR | Zbl
[28] Zakharov L. E., The theory of variances of equilibrium reconstruction, 2007 http://w3.pppl.gov/<nobr>$\sim$</nobr>zakharov