The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. (English) Zbl 1091.35044

The paper studies the Riemann problem for fluid flow in a nozzle. The system prescribing the motion is a nonstrictly hyperbolic system of partial differential equations. The cross-section of the nozzle is variable. Particularly, the section of the nozzle can be assumed to have discontinuity. In this case the right-hand side of an equation of the system contains a Dirac function. In the paper the authors study the existence of solutions in different cases, and show that for different initial data the system may have three, one or zero solutions. Some numerical plot of these solutions is also included in the paper.


35L80 Degenerate hyperbolic equations
35L65 Hyperbolic conservation laws
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76L05 Shock waves and blast waves in fluid mechanics
35L67 Shocks and singularities for hyperbolic equations
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