Tricomi Problem for a Mixed Parabolic--Hyperbolic Equation in a Rectangular Domain
Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 273-279.

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For a class of equations of mixed type, we study an analog of the Dirichlet problem satisfying the conjugation conditions on the line of change of the type. We establish a uniqueness and existence criterion for the solution of this problem.
Keywords: Tricomi problem, mixed parabolic–hyperbolic equation, Dirichlet problem.
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K. B. Sabitov. Tricomi Problem for a Mixed Parabolic--Hyperbolic Equation in a Rectangular Domain. Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 273-279. http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a9/

[1] I. M. Gelfand, “Nekotorye voprosy analiza i differentsialnykh uravnenii”, UMN, 14:3 (1959), 3–19 | MR | Zbl

[2] G. M. Struchina, “Zadacha o sopryazhenii dvukh uravnenii”, Inzhenerno-fizicheskii zhurnal, 4:11 (1961), 99–104

[3] Ya. S. Uflyand, “K voprosu o rasprostranenii kolebanii v sostavnykh elektricheskikh liniyakh”, Inzhenerno-fizicheskii zhurnal, 7:1 (1964), 89–92

[4] L. A. Zolina, “O kraevoi zadache dlya modelnogo uravneniya giperbolicheskogo tipa”, ZhVM i MF, 6:6 (1966), 991–1001 | MR | Zbl

[5] Kh. G. Bzhikhatlov, A. M. Nakhushev, “Ob odnoi kraevoi zadache dlya uravneniya smeshannogo tipa”, Dokl. AN SSSR, 183:2 (1968), 261–264 | MR | Zbl

[6] V. A. Eleev, “O nekotorykh kraevykh zadachakh so smescheniem dlya odnogo uravneniya smeshannogo parabolo-giperbolicheskogo tipa”, Differents. uravneniya, 14:1 (1978), 22–29 | MR | Zbl

[7] T. D. Dzhuraev, Kraevye zadachi dlya uravnenii smeshannogo i smeshanno-sostavnogo tipov, Izd-vo “Fan”, Tashkent, 1979 | MR | Zbl

[8] T. D. Dzhuraev, A. Sopuev, A. Mamazhanov, Kraevye zadachi dlya uravnenii parabolo-giperbolicheskogo tipa, Izd-vo “Fan”, Tashkent, 1986 | MR | Zbl

[9] N. Yu. Kapustin, “Zadacha Trikomi dlya parabolo-giperbolicheskogo uravneniya s vyrozhdayuscheisya giperbolicheskoi chastyu. I”, Differents. uravneniya, 23:1 (1987), 72–78 | MR | Zbl

[10] K. B. Sabitov, “K teorii uravnenii parabolo-giperbolicheskogo tipa so spektralnym parametrom”, Differents. uravneniya, 25:1 (1989), 117–126 | MR | Zbl

[11] N. Yu. Kapustin, E. I. Moiseev, “O skhodimosti spektralnykh razlozhenii funktsii iz klassa Gëldera dlya dvukh zadach so spektralnym parametrom v granichnom uslovii”, Differents. uravneniya, 36:8 (2000), 1069–1074 | MR | Zbl

[12] E. I. Moiseev, “O razreshimosti odnoi nelokalnoi kraevoi zadachi”, Differents. uravneniya, 37:11 (2001), 1565–1567 | MR | Zbl

[13] K. B. Sabitov, Uravneniya matematicheskoi fiziki, Vysshaya shkola, M., 2003

[14] V. A. Chernyatin, “O neobkhodimykh i dostatochnykh usloviyakh suschestvovaniya klassicheskogo resheniya smeshannoi zadachi dlya odnomernogo volnovogo uravneniya”, Dokl. AN SSSR, 287:5 (1986), 1080–1083 | MR | Zbl