A characteristic boundary problem for a~third-order equation with a~psedoparabolic operator where the desired function has shifted arguments
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 54-60.

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

We consider one variant of the Goursat problem for a third-order equation which was not studied earlier and prove its unique solvability.
Keywords: desired function with shifted arguments, pseudo-parabolic operator.
@article{IVM_2014_2_a6,
     author = {E. A. Utkina},
     title = {A characteristic boundary problem for a~third-order equation with a~psedoparabolic operator where the desired function has shifted arguments},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--60},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_2_a6/}
}
TY  - JOUR
AU  - E. A. Utkina
TI  - A characteristic boundary problem for a~third-order equation with a~psedoparabolic operator where the desired function has shifted arguments
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 54
EP  - 60
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_2_a6/
LA  - ru
ID  - IVM_2014_2_a6
ER  - 
%0 Journal Article
%A E. A. Utkina
%T A characteristic boundary problem for a~third-order equation with a~psedoparabolic operator where the desired function has shifted arguments
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 54-60
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_2_a6/
%G ru
%F IVM_2014_2_a6
E. A. Utkina. A characteristic boundary problem for a~third-order equation with a~psedoparabolic operator where the desired function has shifted arguments. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 54-60. http://geodesic.mathdoc.fr/item/IVM_2014_2_a6/

[1] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR | Zbl

[2] Myshkis A. D., “O nekotorykh problemakh teorii differentsialnykh uravnenii s otklonyayuschimsya argumentom”, UMN, 32:2 (1977), 173–202 | MR | Zbl

[3] Azbelev N. V., Rakhmatullina L. F., “Funktsionalno-differentsialnye uravneniya”, Differents. uravneniya, 14:5 (1978), 771–797 | MR | Zbl

[4] Kheili Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR

[5] Mokeichev V. S., Differentsialnye uravneniya s otklonyayuschimsya argumentom, Izd-vo Kazansk. un-ta, Kazan, 1985

[6] Zarubin A. N., Uravneniya smeshannogo tipa s zapazdyvayuschim argumentom, Uchebnoe posobie, OGU, Orel, 1997

[7] Zhegalov V. I., “Giperbolicheskoe uravnenie so smescheniem argumentov iskomoi funktsii”, Uravneniya smeshannogo tipa i rodstvennye problemy analiza i informatiki, Materialy vtorogo Mezhdunarodnogo Rossiisko-Uzbekskogo simpoziuma, Izd-vo KBNTs RAN, Nalchik, 2012, 107–109

[8] Andreev A. A., “O korrektnosti nachalnykh zadach dlya nekotorykh uravnenii v chastnykh proizvodnykh s otklonyayuschimsya argumentom”, Uravneniya neklassicheskogo tipa, Cb., IM SOAN SSSR, Novosibirsk, 1986, 10–14

[9] Andreev A. A., “Ob analogakh klassicheskikh kraevykh zadach dlya odnogo differentsialnogo uravneniya vtorogo poryadka s otklonyayuschimsya argumentom”, Differents. uravneniya, 40:5 (2004), 1126–1128 | Zbl

[10] Andreev A. A., Saushkin I. N., “Ob analoge zadachi Trikomi dlya odnogo modelnogo uravneniya s involyutivnym otkloneniem v beskonechnoi oblasti”, Vestn. Samarsk. tekhn. un-ta. Ser. Fiz.-matem. nauki, 2005, no. 34, 10–16

[11] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vyssh. shkola, M., 1995, 301 pp. | Zbl

[12] Zhegalov V. I., Utkina E. A., “Ob odnom psevdoparabolicheskom uravnenii tretego poryadka”, Izv. vuzov. Matem., 1999, no. 10, 73–76 | MR | Zbl

[13] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976, 544 pp. | MR