Abstract
We construct the solution of the Riemann problem for 2 × 2 isothermal gas dynamics in a duct with discontinuous diameter. Besides shocks and rarefaction, there are standing waves. The solution exists globally. It is obtained as an asymptotic solution for an appropriate Cauchy problem with continuous data. In certain cases bifurcation occurs and there are three solutions, one of which is unstable. This is an example of a Riemann problem whose solution depends discontinuously on the initial data.
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