Geodesic
Local and nonlocal value boundary problems for a third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 117 (2008) no. 2, pp. 21-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The existence and uniqueness of local and nonlocal value boundary problems for third-order mixed-type equations with multiple characteristics is proved. Uniqueness of the problem solution is proved with energy-integral method. The existence of the solution is proved with equivalent reduction method to Fredholm integral equations of the second kind with the help of Green's function.
Keywords: local value boundary problem, nonlocal value boundary problem, mixed-type equations, Green's function, Fredholm integral equation. 
@article{VSGTU_2008_117_2_a2,
     author = {Zh. A. Balkizov},
     title = {Local and nonlocal value boundary problems for a~third-order mixed-type equation equipped with {Tricomi} operator in its hyperbolic part},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {21--28},
     year = {2008},
     volume = {117},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2008_117_2_a2/}
}
TY  - JOUR
AU  - Zh. A. Balkizov
TI  - Local and nonlocal value boundary problems for a third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2008
SP  - 21
EP  - 28
VL  - 117
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2008_117_2_a2/
LA  - ru
ID  - VSGTU_2008_117_2_a2
ER  - 
%0 Journal Article
%A Zh. A. Balkizov
%T Local and nonlocal value boundary problems for a third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2008
%P 21-28
%V 117
%N 2
%U http://geodesic.mathdoc.fr/item/VSGTU_2008_117_2_a2/
%G ru
%F VSGTU_2008_117_2_a2
Zh. A. Balkizov. Local and nonlocal value boundary problems for a third-order mixed-type equation equipped with Tricomi operator in its hyperbolic part. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 117 (2008) no. 2, pp. 21-28. http://geodesic.mathdoc.fr/item/VSGTU_2008_117_2_a2/

[1] Lerner M. E., Repin O. A., “O zadachakh tipa zadachi Franklya dlya nekotorykh ellipticheskikh uravnenii s vyrozhdeniem raznogo roda”, Differents. uravneniya, 35:8 (1999), 1087–1093 | MR | Zbl

[2] Lerner M. E., Repin O. A., “Ob odnoi zadache s dvumya nelokalnymi kraevymi usloviyami dlya uravneniya smeshannogo tipa”, Sib. matem. zhurn., 40:6 (1999), 1260–1275 | MR | Zbl

[3] Sabitov K. B., Sidorenko O. G., “Ob odnoznachnoi razreshimosti nelokalnoi zadachi dlya vyrozhdayuschegosya ellipticheskogo uravneniya spektralnym metodom”, Spektralnaya teoriya differentsialnykh operatorov i rodstvennye problemy, Tr. Mezhdunar. nauchn. konf., T. 1, Sterlitamak, 2003, 213–219

[4] Sabitov K. B., Sidorenko O. G., “Nelokalnaya zadacha dlya vyrozhdayuschegosya giperbolicheskogo uravneniya”, Spektralnaya teoriya differentsialnykh operatorov i rodstvennye problemy, Tr. Mezhdunar. nauchn. konf., T. 1, Sterlitamak, 2004, 80–86

[5] Rakhmanova L. Kh., “Reshenie nelokalnoi zadachi spektralnym metodom dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa v pryamougolnoi oblasti”, Izv. vuzov. Matem., 2007, no. 11, 36–40 | MR

[6] Trikomi F., Lektsii po uravneniyam s chastnymi proizvodnymi, IL, M., 1957, 443 pp.

[7] Nakhushev A. M., Elementy drobnogo ischisleniya i ikh primenenie, KBNTs RAN, Nalchik, 2000, 298 pp.

[8] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 498 pp. | MR

[9] Faddeev D. K., Lektsii po algebre, Lan, SPb., 2002, 416 pp., ISBN 5–8114–0447–6 | MR

[10] Irgashev Yu., “Nekotorye kraevye zadachi dlya uravnenii tretego poryadka s kratnymi kharakteristikami”, Kraevye zadachi dlya differentsialnykh uravnenii i ikh prilozheniya, Fan, Tashkent, 1976, 17–27