Geodesic
A method for an approximate solution of an inverse problem for a semilinear hyperbolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 111-126
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_2003_43_1_a8,
     author = {A. Yu. Shcheglov},
     title = {A method for an approximate solution of an inverse problem for a semilinear hyperbolic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {111--126},
     year = {2003},
     volume = {43},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a8/}
}
TY  - JOUR
AU  - A. Yu. Shcheglov
TI  - A method for an approximate solution of an inverse problem for a semilinear hyperbolic equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2003
SP  - 111
EP  - 126
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a8/
LA  - ru
ID  - ZVMMF_2003_43_1_a8
ER  - 
%0 Journal Article
%A A. Yu. Shcheglov
%T A method for an approximate solution of an inverse problem for a semilinear hyperbolic equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2003
%P 111-126
%V 43
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a8/
%G ru
%F ZVMMF_2003_43_1_a8
A. Yu. Shcheglov. A method for an approximate solution of an inverse problem for a semilinear hyperbolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 111-126. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a8/

[1] Romanov V. G., Nekotorye obratnye zadachi dlya uravnenii giperbolicheskogo tipa, Nauka, M., 1969 | MR

[2] Lavrentev M. M., Reznitskaya K. G., Yakhno V. G., Odnomernye obratnye zadachi matematicheskoi fiziki, Nauka, Novosibirsk, 1982 | MR

[3] Cannon J. R., DuChateau P., “An inverse problem for an unknown source term in a wave equation”, SIAM J. Appl. Math., 43:3 (1983), 553–564 | DOI | MR | Zbl

[4] Denisov A. M., “Edinstvennost resheniya nekotorykh obratnykh zadach neravnovesnoi dinamiki sorbtsii”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1986, no. 2, 25–30 | MR | Zbl

[5] Cavaterra C., “An inverse problem for a semilinear wave equation”, Boll. Univ. Mat. Ital. B. Ser. 7, 2:3 (1988), 695–711 | MR | Zbl

[6] Kabanikhin S. I., Proektsionno-raznostnye metody opredeleniya koeffitsientov giperbolicheskikh uravnenii, Nauka, Novosibirsk, 1988 | MR | Zbl

[7] Baev A. V., “O reshenii obratnoi zadachi dlya volnovogo uravneniya po informatsii, zadannoi v tochke”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1989, no. 4, 28–33 | MR | Zbl

[8] Grasselli M., “Local existence and uniqueness for a quasilinear hyperbolic inverse problem”, J. Appl. Analys., 32:1 (1989), 15–30 | DOI | MR | Zbl

[9] Guo Bao Qu, Wang Jian Tao, “An inverse problem for a one-dimensional semilinear hyperbolic equation with an unknown source”, J. Harbin Inst. Techn., 1989, no. 4, 14–20 | MR | Zbl

[10] Zhang Guan Quan, “On an inverse problem for 1-dimensional wave equation”, Sci. China. Ser. A. Math., Phys., Astron. and Techn. Sci., 32:3 (1989), 257–274 | MR | Zbl

[11] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, Izd-vo MGU, M., 1994

[12] Denisov A. M., “Edinstvennost resheniya zadachi opredeleniya nelineinogo koeffitsienta sistemy uravnenii v chastnykh proizvodnykh v malom i tselom”, Sibirskii matem. zhurnal, 36:1 (1995), 60–71 | MR | Zbl

[13] Karchevsky A. L., “Properties of the misfit functional for a nonlinear one-dimensional coefficient hyperbolic inverse problem”, J. Inv. Ill-Posed Problems, 5:2 (1997), 139–163 | DOI | MR | Zbl

[14] Baev A. V., Soltan I. E., “Obratnaya zadacha prognozirovaniya neodnorodnoi sredy po dannym vertikalno seismicheskogo profilirovaniya”, Zh. vychisl. matem. i matem. fiz., 37:6 (1997), 723–732 | MR | Zbl

[15] Denisov A. M., “Determination of a nonlinear coefficient in a hyperbolic equation for the Goursat problem”, J. Inv. Ill-Posed Problems, 6:4 (1998), 327–334 | DOI | MR | Zbl

[16] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for solving inverse problems in mathematical physics, Marcel Dekker, New York–Basel, 1999 | MR

[17] Denisov A. M., Elements of the theory of inverse problems, VSP, Utrecht, 1999 | MR | Zbl

[18] Lattès R., Lions J.-L., Méthode de quasi-rèversibilité et applications, Dunod, Paris, 1967 | MR

[19] Kaliski S., “Integral theorems for the wave-type heat conductivity equation”, Bull. Acad. Polon. Ser. Sci. Techn., 1969, no. 17, 509–518 | MR | Zbl

[20] Volkov I. A., Svyaz mezhdu resheniyami klassa kraevykh zadach dlya uravneniya teploprovodnosti i volnovogo uravneniya, Nauk. dumka, Kiev, 1977 | MR

[21] Bubnov V. A., Solovev I. A., “Ob ispolzovanii giperbolicheskogo uravneniya v teorii teploprovodnosti”, Inzh.-fiz. zhurnal, 33:6 (1977), 1131–1135 | MR

[22] Shatalov Yu. S., Fomin V. I., Optimalnye integralnye formuly dlya koeffitsientov giperbolicheskikh uravnenii teploprovodnosti, Permskii politekhn. in-t, Perm, 1984 | MR

[23] Elden L., “Hyperbolic approximations for a Cauchy problem for the heat equation”, J. Inv. Problems, 4:1 (1988), 59–70 | DOI | MR | Zbl

[24] Friedman A., Blow-up of solutions of nonlinear heat and wave equations, Dekker Publs., New York, 1991 | MR

[25] Scheglov A. Yu., “Metod priblizhennogo resheniya odnoi obratnoi zadachi dlya uravneniya teploprovodnosti”, Zh. vychisl. matem. i matem. fiz., 32:6 (1992), 904–916 | MR

[26] Savateev E. G., Slynko O. M., “Korrektnost i kachestvennye svoistva zadachi opredeleniya funktsii istochnika giperbolicheskogo uravneniya teploprovodnosti”, Aktualnye probl. sovrem. matem., 1995, no. 1, 134–142 | Zbl

[27] Ishmukhametov A. Z., “Upravlyaemost giperbolicheskikh sistem pri singulyarnykh vozmuscheniyakh”, Differents. ur-niya, 36:2 (2000), 241–250 | MR | Zbl

[28] Scheglov A. Yu., “Metod priblizhennogo resheniya v $C^2$ uravneniya giperbolicheskogo tipa s lipshitsevoi nelineinostyu”, Zh. vychisl. matem. i matem. fiz., 41:3 (2001), 420–435 | Zbl