Abstract: We study the Riemann problem for isothermal flow of a gas in a thin pipe with a kink in it. This is modeled by a $2\times 2$ system of conservation laws with Dirac measure sink term concentrated at the location of the bends in the pipe. We show that the Riemann problem for this system of equations always has a unique solution, given an extra condition relating the speeds on both sides of the kink. Furthermore, we study the related problem where the flow is perturbed by an continuous addition of momentum at distinct points. Under certain conditions we show that also this Riemann problem has a unique solution.
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