Geodesic
Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 68-80 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides. We obtain the conditions of a nonlocal solvability of this Cauchy problem. The study of the nonlocal solvability of the Cauchy problem for a system of two quasilinear differential equations with special right-hand sides is based on the method of an additional argument. The proof of the nonlocal resolvability of the Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides relies on global estimates.
Keywords: first order partial differential equations, Cauchy problem, the method of an additional argument. 
@article{UFA_2014_6_4_a5,
     author = {M. V. Dontsova},
     title = {Nonlocal solvability conditions for {Cauchy} problem for a~system of first order partial differential equations with special right-hand sides},
     journal = {Ufa mathematical journal},
     pages = {68--80},
     year = {2014},
     volume = {6},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a5/}
}
TY  - JOUR
AU  - M. V. Dontsova
TI  - Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides
JO  - Ufa mathematical journal
PY  - 2014
SP  - 68
EP  - 80
VL  - 6
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a5/
LA  - en
ID  - UFA_2014_6_4_a5
ER  - 
%0 Journal Article
%A M. V. Dontsova
%T Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides
%J Ufa mathematical journal
%D 2014
%P 68-80
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a5/
%G en
%F UFA_2014_6_4_a5
M. V. Dontsova. Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 68-80. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a5/

[1] Rozhdestvenskii B. L., Yanenko N. I., Sistemy kvazilineinykh uravnenii i ikh prilozheniya v gazovoi dinamike, Nauka, M., 1978, 592 pp. | MR

[2] Imanaliev M. I., Pankov P. S., Alekseenko S. N., “Metod dopolnitelnogo argumenta”, Vestnik KazNU. Ceriya “Matematika, mekhanika, informatika” (Almaty), 2006, no. 1, Spets. vypusk, 60–64

[3] Alekseenko S. N., Shemyakina T. A., Dontsova M. V., “Usloviya nelokalnoi razreshimosti sistem differentsialnykh uravnenii v chastnykh proizvodnykh pervogo poryadka”, Nauchno-tekhnicheskie vedomosti SPbGPU. Fiziko-matematicheskie nauki, 2013, no. 3(177), 190–201

[4] Dontsova M. V., “Issledovanie razreshimosti sistemy differentsialnykh uravnenii v chastnykh proizvodnykh pervogo poryadka so svobodnymi chlenami”, Materialy Mezhdunarodnogo molodezhnogo nauchnogo foruma “LOMONOSOV-2014”, MAKS Press, M., 2014, 1 elektron. opt. disk (DVD-ROM)

[5] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987, 840 pp. | MR

[6] Frankl F. I., Izbrannye trudy po gazovoi dinamike, Nauka, M., 1973, 712 pp. | MR

[7] Shemyakina T. A., “Teorema suschestvovaniya ogranichennogo resheniya zadachi Koshi dlya sistemy Franklya giperbolicheskogo tipa”, Nauchno-tekhnicheskie vedomosti SPbGPU. Fiziko-matematicheskie nauki, 2012, no. 2(146), 130–131

[8] Alekseenko S. N., Dontsova M. V., “Issledovanie razreshimosti sistemy uravnenii, opisyvayuschei raspredelenie elektronov v elektricheskom pole spraita”, Matem. vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona, 14, VyatGGU, Kirov, 2012, 34–41

[9] Alekseenko S. N., Dontsova M. V., “Lokalnoe suschestvovanie ogranichennogo resheniya sistemy uravnenii, opisyvayuschei raspredelenie elektronov v slaboionizirovannoi plazme v elektricheskom pole spraita”, Matem. vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona, 15, VyatGGU, Kirov, 2013, 52–59

[10] Dontsova M. V., “Usloviya lokalnoi razreshimosti zadachi Koshi dlya sistemy uravnenii, opisyvayuschei raspredelenie elektronov v slaboionizirovannoi plazme v elektricheskom pole spraita”, XVIII Nizhegorodskaya sessiya molodykh uchenykh. Estestvennye, matematicheskie nauki (28–31 maya 2013 g.), NIU RANKhIGS, N. Novgorod, 2013, 183–185

[11] Imanaliev M. I., Ved Yu. A., “O differentsialnom uravnenii v chastnykh proizvodnykh pervogo poryadka s integralnym koeffitsientom”, Differentsialnye uravneniya, 25:3 (1989), 465–477 | MR | Zbl

[12] Imanaliev M. I., Alekseenko S. N., “K teorii sistem nelineinykh integro-differentsialnykh uravnenii v chastnykh proizvodnykh tipa Uizema”, Doklady AN SSSR, 325:6 (1982), 1111–1115 | MR

[13] Imanaliev M. I., Alekseenko S. N., “K voprosu suschestvovaniya gladkogo ogranichennogo resheniya dlya sistemy dvukh nelineinykh differentsialnykh uravnenii v chastnykh proizvodnykh pervogo poryadka”, Doklady RAN, 379:1 (2001), 16–21 | MR | Zbl