Characteristic boundary-value problem for a~system of first-order partial differential equations with a~shift of arguments of the sought-for function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 63-68.

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For a system of first-order partial differential equations in a form not investigated earlier, we consider a variant of the Goursat problem and prove the existence and uniqueness of the problem.
Keywords: system of equations with a shift of arguments of sought-for function, system of functional differential equations
Mots-clés : Goursat problem.
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E. A. Utkina. Characteristic boundary-value problem for a~system of first-order partial differential equations with a~shift of arguments of the sought-for function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 63-68. http://geodesic.mathdoc.fr/item/IVM_2015_7_a6/

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

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

[6] 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

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

[8] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Introduction to the theory of functional differential equations: methods and applications, Hindawi Publishing Corporation, New York, 2007 | MR | Zbl

[9] Zhegalov V. I., “Kharakteristicheskaya granichnaya zadacha dlya giperbolicheskogo uravneniya so smescheniem argumentov iskomoi funktsii”, Dokl. RAN, 146:5 (2012), 490–493 | MR

[10] Utkina E. A., “Kharakteristicheskaya granichnaya zadacha dlya uravneniya tretego poryadka s psevdoparabolicheskim operatorom i so smescheniem argumentov iskomoi funktsii”, Izv. vuzov. Matem., 2014, no. 2, 54–60 | Zbl

[11] Chekmarev T. V., “Formuly resheniya zadachi Gursa dlya odnoi sistemy uravnenii s chastnymi proizvodnymi”, Differents. uravneniya, 18:9 (1982), 1614–1622 | MR

[12] Utkina E. A., “Zadacha so smescheniyami dlya trekhmernogo uravneniya Bianki”, Differents. uravneniya, 46:4 (2010), 535–539 | MR | Zbl

[13] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

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