A Riemann problem in gas dynamics with bifurcation. (English) Zbl 0611.35060
The authors construct the solution of the Riemann problem for the one- dimensional isothermal equations of gas dynamics in a duct with discontinuous cross section. The solution exists globally. Besides shocks and rarefaction waves there are standing waves in the solution. The solution is obtained as a weak limit of a sequence of solutions to appropriate Cauchy problems with continuous data. Sometimes bifurcation occurs and there are tree solutions, one of which is unstable. This is an interesting example of a Riemann problem whose solution depends discontinuously on the initial data.
Reviewer: J.Wang
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35B32 | Bifurcations in context of PDEs |
| 76N15 | Gas dynamics (general theory) |
| 35L67 | Shocks and singularities for hyperbolic equations |
Keywords:
Riemann problem; isothermal equations; gas dynamics; discontinuous cross section; shocks; rarefaction waves; standing waves; Cauchy problems; bifurcationReferences:
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