Abstract:
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.
Citation:
A. I. Vol'pert, S. I. Khudyaev, “On the Cauchy problem for composite systems of nonlinear differential equations”, Math. USSR-Sb., 16:4 (1972), 517–544
\Bibitem{VolKhu72}
\by A.~I.~Vol'pert, S.~I.~Khudyaev
\paper On the Cauchy problem for composite systems of nonlinear differential equations
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 4
\pages 517--544
\mathnet{http://mi.mathnet.ru/eng/sm3138}
\crossref{https://doi.org/10.1070/SM1972v016n04ABEH001438}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=390528}
\zmath{https://zbmath.org/?q=an:0239.35017}
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https://www.mathnet.ru/eng/sm3138
https://doi.org/10.1070/SM1972v016n04ABEH001438
https://www.mathnet.ru/eng/sm/v129/i4/p504
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