Geodesic
On a problem with shift for mixed type equation with two degeneration lines
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 53-59.

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

For mixed type equation with two perpendicular lines of degeneracy we consider the boundary-value problem with nonlocal condition, connecting with the help of generalized operators of fractional integro-differentiation the trace of the normal derivative of the unknown function on the transition line and its own trace on the control characteristics and the line of degeneracy. The author proves the unique solvability of the problem.
Keywords: mixed type equations, nonlocal problem, operator of fractional integration, operator of fractional differentiation, Cauchy problem, Gauss hypergeometric function, Fredholm's integral equation. 
@article{IVM_2017_1_a5,
     author = {O. A. Repin},
     title = {On a problem with shift for mixed type equation with two degeneration lines},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--59},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_1_a5/}
}
TY  - JOUR
AU  - O. A. Repin
TI  - On a problem with shift for mixed type equation with two degeneration lines
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 53
EP  - 59
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_1_a5/
LA  - ru
ID  - IVM_2017_1_a5
ER  - 
%0 Journal Article
%A O. A. Repin
%T On a problem with shift for mixed type equation with two degeneration lines
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 53-59
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_1_a5/
%G ru
%F IVM_2017_1_a5
O. A. Repin. On a problem with shift for mixed type equation with two degeneration lines. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 53-59. http://geodesic.mathdoc.fr/item/IVM_2017_1_a5/

[1] Saigo M., “A remark on integral operators involving the Gauss hypergeometric function”, Math. Rep. Kyushu Univ., 11:2 (1978), 135–143 | MR | Zbl

[2] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987

[3] Trikomi F., O lineinykh uravneniyakh v chastnykh proizvodnykh vtorogo poryadka smeshannogo tipa, GITTL, M., 1947

[4] Repin O. A., Shuvalova T. V., “Nelokalnaya kraevaya zadacha dlya uravneniya smeshannogo tipa s dvumya liniyami vyrozhdeniya”, Differents. uravneniya, 44:6 (2008), 848–851 | MR | Zbl

[5] Kilbas A. A., Repin O. A., “O razreshimosti kraevoi zadachi dlya uravneniya smeshannogo tipa s chastnoi drobnoi proizvodnoi Rimana–Liuvillya”, Differents. uravneniya, 46:10 (2010), 1453–1460 | MR | Zbl

[6] Tersenov S. A., Vvedenie v teoriyu uravnenii vyrozhdayuschikhsya na granitse, NGU, Novosibirsk, 1973 | MR

[7] Gordeev A. M., “Nekotorye kraevye zadachi dlya obobschennogo uravneniya Eilera–Puassona–Darbu”, Volzhsk. matem. sb., 1968, no. 6, 56–61 | MR | Zbl

[8] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Dopolnitelnye glavy, Nauka, M., 1986

[9] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973 | MR

[10] Marichev O. I., Metod vychisleniya integralov ot spetsialnykh funktsii, Nauka i tekhnika, Minsk, 1978 | MR

[11] Saigo M., Kilbas A. A., “Generalized fractional integrals and derivatives in Hölder space”, Transforms methods special functions, Proc. Intern. Workshop (Sofia, August 12–17, 1995), Singapore, 1995, 282–293 | Zbl

[12] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shkola, M., 1985

[13] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968