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 X 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 a continuous addition of momentum at distinct points. Under certain conditions we show that this Riemann problem alsohas a unique solution.

MSC codes

  1. 35L65
  2. 45L67
  3. 76N15

Keywords

  1. Riemann problem
  2. isothermal gas dynamics
  3. nonlinear resonance

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Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 497 - 515
ISSN (online): 1095-7154

History

Published online: 1 August 2006

MSC codes

  1. 35L65
  2. 45L67
  3. 76N15

Keywords

  1. Riemann problem
  2. isothermal gas dynamics
  3. nonlinear resonance

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