Geodesic
On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domai
Matematičeskie zametki, Tome 92 (2012) no. 1, pp. 74-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study the boundary-value problem for an equation of mixed type with singular coefficient. The uniqueness of the solution of the problem is proved using the extremum principle and the existence of a solution to the problem is established by the method of integral equations.
Keywords: partial differential equation of mixed type, Gellerstedt problem, boundary-value problem, parabolic degeneracy, extremum principle, Cauchy problem, Darboux formula. 
@article{MZM_2012_92_1_a7,
     author = {M. Kh. Ruziev},
     title = {On the {Boundary-Value} {Problem} for a {Class} of {Equations} of {Mixed} {Type} in an {Unbounded} {Domai}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {74--83},
     publisher = {mathdoc},
     volume = {92},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_1_a7/}
}
TY  - JOUR
AU  - M. Kh. Ruziev
TI  - On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domai
JO  - Matematičeskie zametki
PY  - 2012
SP  - 74
EP  - 83
VL  - 92
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_1_a7/
LA  - ru
ID  - MZM_2012_92_1_a7
ER  - 
%0 Journal Article
%A M. Kh. Ruziev
%T On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domai
%J Matematičeskie zametki
%D 2012
%P 74-83
%V 92
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_1_a7/
%G ru
%F MZM_2012_92_1_a7
M. Kh. Ruziev. On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domai. Matematičeskie zametki, Tome 92 (2012) no. 1, pp. 74-83. http://geodesic.mathdoc.fr/item/MZM_2012_92_1_a7/

[1] S. Gellerstedt, “Quelques problèmes mixtes pour l'èquation $y^m z_{xx}+z_{yy}=0$”, Arkiv Mat. Astron. Fys. A, 26:3 (1937), 1–32 | Zbl

[2] Yu. M. Krikunov, “Ob odnoi zadache Gellerstedta”, Izv. vuzov. Matem., 1975, no. 6, 56–59 | MR | Zbl

[3] I. E. Solodovnikov, “Obobschennaya zadacha Gellerstedta dlya odnogo chastnogo sluchaya uravneniya $k(y)u_{xx}+u_{yy}=0$”, Tr. sem. po kraev. zadacham, 10, Izd-vo Kazanskogo un-ta, Kazan, 1973, 130–139 | MR | Zbl

[4] A. V. Bitsadze, “Ob odnoi zadachi Franklya”, Dokl. AN SSSR, 109:6 (1956), 1091–1094 | MR | Zbl

[5] Yu. Devingtal, “O s uschestvovanii i edinstvennosti resheniya odnoi zadachi F. I. Franklya”, Izv. vuzov. Matem., 1958, no. 2, 39–51 | MR | Zbl

[6] V. I. Zhegalov, “Zadacha Franklya so smescheniem”, Izv. vuzov. Matem., 1979, no. 9, 11–20 | MR | Zbl

[7] N. Yu. Kapustin, K. B. Sabitov, “O reshenii odnoi problemy v teorii zadachi Franklya dlya uravnenii smeshannogo tipa”, Dokl. AN SSSR, 317:5 (1991), 1048–1052 | MR | Zbl

[8] M. S. Salakhitdinov, M. Mirsaburov, “Zadacha s nelokalnym granichnym usloviem na kharakteristike dlya odnogo klassa uravnenii smeshannogo tipa”, Matem. zametki, 86:5 (2009), 748–760 | MR | Zbl

[9] M. Mirsaburov, M. Kh. Ruziev, “Zadacha s nelokalnymi usloviyami na linii vyrozhdeniya i na parallelnykh kharakteristikakh dlya odnogo klassa uravnenii smeshannogo tipa”, Uzbeksk. matem. zhurn., 2009, no. 3, 107–116 | MR

[10] M. M. Smirnov, Uravneniya smeshannogo tipa, Vysshaya shkola, M., 1985 | MR

[11] M. S. Salakhitdinov, M. Mirsaburov, Nelokalnye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami, Izd-vo NUUz, Tashkent, 2005

[12] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya. Granichnye zadachi teorii funktsii i nekotorye ikh prilozheniya k matematicheskoi fizike, Nauka, M., 1968 | MR | Zbl

[13] F. D. Gakhov, Yu. I. Cherskii, Uravneniya tipa svertki, Nauka, M., 1978 | MR | Zbl