Mathematics of the USSR-Sbornik · 1972 · 214 citations · 0 references
Compressible FlowFirst OrderEngineeringSingularly Perturbed ProblemHyperbolic-parabolic Composite SystemsFluid MechanicsHyperbolic Conservation LawParabolic EquationOscillation TheoryNonlinear EquationsNonlinear EquationNonlinear Hyperbolic ProblemFunctional AnalysisHyperbolic EquationNonlinear Mechanical SystemNonlinear Functional Analysis
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 items.