Geodesic
Dirichlet problem for loaded equation of Lavrentiev–Bizadze
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 39-47 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Necessary and sufficient conditions of the uniqueness of solution of the first boundary problem for the loaded equtation of Lavrentiev–Bitsadze in the rectangular area are established in this work.The solution of the task in view is constructed in the form of the number sum on the own functions of a corresponding one-dimensional problem on the own values.
Keywords: loaded equation of the mixed type, Dirichlet problem, spectral method, uniqueness
Mots-clés : existence. 
@article{VSGU_2010_6_a4,
     author = {E. P. Melisheva},
     title = {Dirichlet problem for loaded equation of {Lavrentiev{\textendash}Bizadze}},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {39--47},
     year = {2010},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2010_6_a4/}
}
TY  - JOUR
AU  - E. P. Melisheva
TI  - Dirichlet problem for loaded equation of Lavrentiev–Bizadze
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2010
SP  - 39
EP  - 47
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VSGU_2010_6_a4/
LA  - ru
ID  - VSGU_2010_6_a4
ER  - 
%0 Journal Article
%A E. P. Melisheva
%T Dirichlet problem for loaded equation of Lavrentiev–Bizadze
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2010
%P 39-47
%N 6
%U http://geodesic.mathdoc.fr/item/VSGU_2010_6_a4/
%G ru
%F VSGU_2010_6_a4
E. P. Melisheva. Dirichlet problem for loaded equation of Lavrentiev–Bizadze. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2010), pp. 39-47. http://geodesic.mathdoc.fr/item/VSGU_2010_6_a4/

[1] Sabitov K. B., “Nachalno-granichnaya zadacha dlya nagruzhennogo uravneniya parabolo-giperbolicheskogo tipa”, Dokl. AMAN. Nalchik, 11:1 (2009), 66–73 | MR

[2] Sabitov K. B., “Zadacha Trikomi dlya uravnenii smeshannogo parabolo-giperbolicheskogo tipa v pryamougolnoi oblasti”, Matematicheskie zametki, 86:2 (2009), 273–279 | DOI | MR | Zbl

[3] Nakhushev A. M., “O zadache Darbu dlya odnogo vyrozhdayuschegosya nagruzhennogo integrodifferentsialnogo uravneniya vtorogo poryadka”, Differentsialnye uravneniya, 12:1 (1976), 103–108 | MR | Zbl

[4] Kaziev V. M., “Zadacha Trikomi dlya nagruzhennogo uravneniya Lavrenteva–Bitsadze”, Differentsialnye uravneniya, 15:1 (1979), 173–175 | MR | Zbl

[5] Nakhushev A. M., “Nagruzhennye uravneniya i ikh prilozheniya”, Differentsialnye uravneniya, 19:1 (1983), 86–94 | MR | Zbl

[6] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995, 301 pp. | Zbl

[7] Dzhenaliev M. T., K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii, Almata, 1995, 270 pp.

[8] Pulkina L. S., “Nelokalnaya zadacha dlya nagruzhennogo giperbolicheskogo uravneniya”, Trudy MIAN, 236 (2002), 298–303 | MR

[9] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp. | Zbl

[10] Kozhanov A. I., “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Vychislitelnaya matematika i matematicheskaya fizika, 44:4 (2004), 694–716 | MR | Zbl

[11] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp.

[12] Khubiev K. U., Lokalnye i nelokalnye kraevye zadachi dlya nagruzhennykh uravnenii smeshannogo giperbolo-parabolicheskogo tipa, avtoref. dis. $\dots$ kand. fiz.-mat. nauk, Belgorod, 2009, 15 pp.