This article is cited in 149 papers

On the Cauchy problem for composite systems of nonlinear differential equations

A. I. Vol'pert, S. I. Khudyaev


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.

UDC: 517.946.8

MSC: Primary 35M05; Secondary 35K55, 80A30, 76W05

Received: 05.04.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 16:4, 517–544

Bibliographic databases:

• 
•