Geodesic
On the Cauchy problem for composite systems of nonlinear differential equations
Sbornik. Mathematics, Tome 16 (1972) no. 4, pp. 517-544 
A. I. Vol'pert; S. I. Khudyaev. On the Cauchy problem for composite systems of nonlinear differential equations. Sbornik. Mathematics, Tome 16 (1972) no. 4, pp. 517-544. http://geodesic.mathdoc.fr/item/SM_1972_16_4_a2/
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     title = {On the {Cauchy} problem for composite systems of nonlinear differential equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the solvability of the Cauchy problem in a space of smooth functions is demonstrated for hyperbolic-parabolic composite systems of nonlinear equations which include a broad class of equations of mathematical physics, in particular, symmetric systems of first order and parabolic systems of second order. Cauchy problems for the equations of the dynamics of a viscous compressible fluid and for the equations of gas dynamics are solved as examples. Bibliography: 6 titles.

[1] L. Nirenberg, “On elliptic partial differential equations”, Ann. Scuta Norm. Sup. Pisa, Ser. 3, 13 (1959), 116–162 | MR

[2] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, 1950

[3] Yu. Mozer, “Bystro skhodyaschiisya metod iteratsii i nelineinye differentsialnye uravneniya”, Uspekhi matem. nauk, XXIII:4(142) (1968), 179–238 | MR

[4] J. Schauder, “Der Fixpunktsatz in Funktionalraumen”, Studia Math., 2 (1930), 171–180 | Zbl

[5] L. D. Landau, E. M. Lifshits, Mekhanika sploshnykh sred, Moskva, Gostekhizdat, 1953

[6] S. K. Godunov, “Interesnyi klass kvazilineinykh sistem”, DAN SSSR, 139:3 (1961), 521–523 | MR | Zbl