Geodesic
On the nonlocal solvability of the Cauchy problem for a matrix system of partial differential equations of Fedorov–Bernulli type
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 48-53 
S. V. Zhestkov; P. P. Zabreiko. On the nonlocal solvability of the Cauchy problem for a matrix system of partial differential equations of Fedorov–Bernulli type. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 48-53. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The nonlocal solvability of the Cauchy problem for a matrix system of partial differential equations of Fedorov–Bernulli type is established. The existence of an invariant Banach space for this system is proved.

[1] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, M., 1977 | MR

[2] Dubinskii Yu.A., Zadacha Koshi v kompleksnoi oblasti, M., 1996

[3] Zhestkov S.V., Zabreiko P.P., “Printsipy Banakha–Kachchioppoli i Kantorovicha dlya zadachi Koshi v teorii nelineinykh sistem s chastnymi proizvodnymi”, Trudy In-ta matematiki NAN Belarusi. Minsk, 4 (2000), 48–53 | Zbl

[4] Zhestkov S.V., Zabreiko P.P., “O printsipe nepodvizhnoi tochki dlya matrichnykh sistem v chastnykh proizvodnykh tipa Fedorova–Rikkati”, Differents. uravneniya, 40:6 (2004), 840–843 | MR | Zbl

[5] Rosinger E.E., Generalized solutions of nonlinear partial differential equations, North-Holland, 1987 | MR | Zbl

[6] Zeitunyan R.Kh., “Nelineinye dlinnye volny na poverkhnosti vody i solitony”, Uspekhi fiz. nauk, 165:12 (1995), 1403–1456

[7] Zhestkov S.V., Zabreiko P.P., “O nelokalnoi razreshimosti zadachi Koshi dlya kvazilineinykh normalnykh sistem v chastnykh proizvodnykh pervogo poryadka”, Differents. uravneniya, 39:7 (2003), 1001–1003 | MR | Zbl

[8] Walter W., “An elementary proof of the Cauchy–Kowalevsky theorem”, Amer. Math. Monthly, 92:2 (1985), 115–126 | DOI | MR | Zbl

[9] Tutschke W., “An abstract non linear Cauchy–Kowalewski theorem and its proof by a contraction-mapping principle”, Mat. vesn., 38:4 (1986), 597–607 | MR | Zbl