Geodesic
Tricomi problem for nonlinear equation of mixed type with functional retarding, advancing and concentrated deviation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 20-29.

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

We investigate the problem for nonlinear mixed-type equation with the Lavrent'ev–Bitsadze operation in the main part and the functional delay and advancing in the lowest terms. We construct the general solution to the equation. The problem is uniquely solvable.
Keywords: mixed-type equation, Riemann's function, integral equations, formulas of mutual treatment, difference equation. 
@article{IVM_2017_11_a2,
     author = {A. N. Zarubin},
     title = {Tricomi problem for nonlinear equation of mixed type with functional retarding, advancing and concentrated deviation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {20--29},
     publisher = {mathdoc},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_11_a2/}
}
TY  - JOUR
AU  - A. N. Zarubin
TI  - Tricomi problem for nonlinear equation of mixed type with functional retarding, advancing and concentrated deviation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 20
EP  - 29
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_11_a2/
LA  - ru
ID  - IVM_2017_11_a2
ER  - 
%0 Journal Article
%A A. N. Zarubin
%T Tricomi problem for nonlinear equation of mixed type with functional retarding, advancing and concentrated deviation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 20-29
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_11_a2/
%G ru
%F IVM_2017_11_a2
A. N. Zarubin. Tricomi problem for nonlinear equation of mixed type with functional retarding, advancing and concentrated deviation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 20-29. http://geodesic.mathdoc.fr/item/IVM_2017_11_a2/

[1] Churikov F. S., Kokinasidi P. D., “O postroenii funktsii Rimana dlya kompaktnykh uravnenii metodom promezhutochnogo argumenta”, Nauchn. tr. Kubansk. un-ta, 1976, no. 222, 5–12

[2] Ter-Krikorov A. M., Shabunin M. I., Kurs matematicheskogo analiza, Nauka, M., 1988

[3] Vekua I. N., Novye metody resheniya ellipticheskikh uravnenii, OGIZ, M.–L., 1948

[4] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983

[5] Zarubin A. N., Uravneniya smeshannogo tipa s zapazdyvayuschim argumentom, Izd-vo Orlovsk. gos. un-ta, Orel, 1999

[6] Frankl F. I., Izbrannye trudy po gazovoi dinamike, Nauka, M., 1973

[7] Zarubin A. N., “Kraevaya zadacha dlya operezhayusche-zapazdyvayuschego uravneniya smeshannogo tipa s negladkoi liniei vyrozhdeniya”, Differents. uravneniya, 50:10 (2014), 1362–1372 | DOI | Zbl

[8] Zarubin A. N., “Kraevaya zadacha dlya uravneniya smeshannogo tipa s operezhayusche-zapazdyvayuschim argumentom”, Differents. uravneniya, 48:10 (2012), 1404–1411 | Zbl

[9] Zarubin A. N., “Zadacha Trikomi dlya operezhayusche-zapazdyvayuschego uravneniya smeshannogo tipa s peremennym otkloneniem argumenta”, Differents. uravneniya, 51:10 (2015), 1315–1327 | DOI | Zbl

[10] Agranovich M. S., Obobschenye funktsii, MTsIMO, M., 2008