Geodesic
Wave bases in multidimensional inverse problems
Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 23-42 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The author gives a detailed account of an approach to multidimensional inverse problems that utilizes ideas and results of the theory of boundary control (J.-L. Lions, D. L. Russell, and others). Within the bounds of a single scheme, formulations of two types are considered: spectral and time-dependent. Multidimensional analogs to the classical Gel'fand–Levitan equations are derived. The potential of the approach and some ideas on numerical realization are discussed. Bibliography: 15 titles. 
@article{SM_1990_67_1_a1,
     author = {M. I. Belishev},
     title = {Wave bases in multidimensional inverse problems},
     journal = {Sbornik. Mathematics},
     pages = {23--42},
     year = {1990},
     volume = {67},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_1_a1/}
}
TY  - JOUR
AU  - M. I. Belishev
TI  - Wave bases in multidimensional inverse problems
JO  - Sbornik. Mathematics
PY  - 1990
SP  - 23
EP  - 42
VL  - 67
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1990_67_1_a1/
LA  - en
ID  - SM_1990_67_1_a1
ER  - 
%0 Journal Article
%A M. I. Belishev
%T Wave bases in multidimensional inverse problems
%J Sbornik. Mathematics
%D 1990
%P 23-42
%V 67
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1990_67_1_a1/
%G en
%F SM_1990_67_1_a1
M. I. Belishev. Wave bases in multidimensional inverse problems. Sbornik. Mathematics, Tome 67 (1990) no. 1, pp. 23-42. http://geodesic.mathdoc.fr/item/SM_1990_67_1_a1/

[1] Belishev M. I., “Ob odnom podkhode k mnogomernym obratnym zadacham dlya volnovogo uravneniya”, DAN SSSR, 297:3 (1987), 524–527 | MR

[2] Russell D. L., “Boundary value control theory of the higher dimensional wave equation”, SIAM J. Control., 9 (1971), 29–42 | DOI | MR | Zbl

[3] Russell D. L., “Controlability and stabilizability theory for linear partial differential equations”, SIAM Review, 20:4 (1978), 639–739 | DOI | MR | Zbl

[4] Lion Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR

[5] Lions J.-L., Magcnes E., Problemes aux limites nonhomogenes et applications, 2, Dunod, Paris, 1968 | Zbl

[6] Landis E. M., “O nekotorykh svoistvakh reshenii ellipticheskikh uravnenii”, DAN SSSR, 107:5 (1956), 640–643 | MR | Zbl

[7] Blagoveschenskii A. S., “O lokalnom metode resheniya nestatsionarnoi obratnoi zadachi dlya neodnorodnoi struny”, Tr. MIAN, 115 (1971), 28–38 | Zbl

[8] Belishev M. I., “Uravneniya tipa Gelfanda–Levitana v mnogomernoi obratnoi zadache dlya volnovogo uravneniya”, Zap. nauch. semin. LOMI, 165:17 (1987), 15–20 | Zbl

[9] Babich V. M., Buldyrev V. S., Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 | MR

[10] Belishev M. I., Kurylev Ya. V., “Obratnaya zadacha akusticheskogo rasseyaniya v prostranstve s lokalnoi neodnorodnostyu”, Matematicheskie voprosy teorii rasprostraneniya voln, Zap. nauch. semin. LOMI, 156, no. 16, 1986, 24–34 | MR | Zbl

[11] Belishev M. I., Kurylev Ya. V., “Nestatsionarnaya obratnaya zadacha dlya mnogomernogo volnovogo uravneniya “v bolshom””, Zap. nauch. semin. LOMI, 165:17 (1987), 21–30 | MR | Zbl

[12] Hormander L., Linear Partial Differential Operators, Springer-Verlag, Heidelberg–Berlin, 1963 | MR

[13] Berezanskii Yu. M., “O teoreme edinstvennosti v obratnoi zadache spektralnogo analiza dlya uravneniya Shredingera”, Tr. MMO, 7 (1958), 3–6

[14] Khaidarov A., “Karlemanovskie otsenki i obratnye zadachi dlya giperbolicheskikh uravnenii vtorogo poryadka”, Matem. sb., 130(172):2(6) (1986), 265–274 | MR | Zbl

[15] Belishev M. I., Blagoveschenskii A. S., “Pryamoi metod resheniya nestatsionarnoi obratnoi zadachi dlya volnovogo uravneniya”, Shkola-seminar po nekorrektnym i obratnym zadacham matem. fiziki, Tez. dokl. (Krasnoyarsk, iyun 1986 g.) | Zbl