Geodesic
On the Cauchy problem for composite systems of nonlinear differential equations
Sbornik. Mathematics, Tome 16 (1972) no. 4, pp. 517-544

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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. 
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     title = {On the {Cauchy} problem for composite systems of nonlinear differential equations},
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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/