Geodesic
Dirichlet problem for loaded degenerating equation of the mixed type in the rectangular area
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2013), pp. 40-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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Necessary and sufficient conditions of the uniqueness of solution of the first boundary problem for the loaded degenerating equtation of Lavrentiev–Bitsadze in rectangular area are established in this work.The solution of the task is constructed in the form of the number sum on the eigen functions of a corresponding one-dimensional problem on the eigen values. The solution stability from boundary functions is showed.
Keywords: loaded degenerating equation of the mixed type, problem of Dirihle, spectral method, uniqueness, stability.
Mots-clés : existence 
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E. P. Melisheva. Dirichlet problem for loaded degenerating equation of the mixed type in the rectangular area. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2013), pp. 40-53. http://geodesic.mathdoc.fr/item/VSGU_2013_6_a4/

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

[2] Sabitov K. B., “Zadacha Trikomi dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa v pryamougolnoi oblasti”, Matematicheskie zametki, 2009, no. 2, 273–279 | DOI | MR

[3] Sabitov K. B., “Zadacha Dirikhle dlya uravneniya smeshannogo tipa v pryamougolnoi oblasti”, DAN, 413:1 (2007), 23–26 | Zbl

[4] Cannon J. R., “Dirihlet problem for an aquation of mixed type with a discontinius coefficient”, Ann. math. pura ed appl., 62 (1963), 371–377 | DOI | MR | Zbl

[5] Shabat B. V., “Primery resheniya zadachi Dirikhle dlya uravneniya smeshannogo tipa”, DAN, 112:3 (1957), 386–389 | MR | Zbl

[6] Khachev M. M., “Zadacha Dirikhle dlya obobschennogo uravneniya Lavrenteva–Bitsadze v pryamougolnoi oblasti”, Differentsialnye uravneniya, 14:1 (1978), 136–139 | MR | Zbl

[7] Zhegalov V. I., “Nelokalnaya zadacha Dirikhle dlya uravneniya smeshannogo tipa”, Neklassicheskie uravneniya matem. fiziki, IM SO AN SSSR, Novosibirsk, 1985, 168–172 | Zbl

[8] Soldatov A. P., “Zadacha Dirikhle dlya uravneniya Lavrenteva–Bitsadze”, Differentsialnye uravneniya, 30:11 (1994), 2001–2009 | MR | Zbl

[9] Sabitova Yu. K., Bakhristova A. A., “Zadacha Dirikhle dlya uravneniya smeshannogo tipa s operatorom Lavrenteva–Bitsadze”, Trudy Sterlitamakskogo filiala Akademii nauk Respubliki Bashkortostan. Ser.: Fiziko-matematicheskie i tekhnicheskie nauki, 6, Gilem, UFA, 2009, 103–110

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

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

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

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

[14] Pulkina L. S., “Nelokalnaya zadacha dlya nagruzhennogo giperbolicheskogo uravneniya”, Trudy MIAN, 236, 2002, 298–303 | Zbl

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

[16] Khubiev K. U., “Ob odnoi kraevoi zadache dlya nagruzhennogo uravneniya smeshannogo giperbolo-parabolicheskogo tipa”, Doklady AMAN, 7:2 (2005), 74–77 | MR | Zbl

[17] Melisheva E. P., “Zadacha Dirikhle dlya nagruzhennogo uravneniya Lavrenteva–Bitsadze”, Vestnik SamGU. Estestvennonauchnaya seriya, 80:6 (2010), 39–47

[18] Sabitov K. B., Melisheva E. P., “Zadacha Dirikhle dlya nagruzhennogo uravneniya smeshannogo tipa v pryamougolnoi oblasti”, Izvestiya vuzov. Ser.: Matematika, 2013 (to appear)

[19] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. 2, Nauka, M., 1966, 296 pp.

[20] Sabitov K. B., Vagapova E. V., “Zadacha Dirikhle dlya uravneniya smeshannogo tipa s dvumya liniyami vyrozhdeniya v pryamougolnoi oblasti”, Differentsialnye uravneniya, 49:1 (2013), 68–78 | MR | Zbl

[21] Sabitov K. B., Sidorenko O. G., “Zadacha s usloviyami periodichnosti dlya vyrozhdayuschegosya uravneniya smeshannogo tipa”, Differentsialnye uravneniya, 46:1 (2010), 105–113 | MR