Methods and Applications of Analysis

Volume 10 (2003)

Number 2

The Generic Solution of the Riemann Problem in a Neighborhood of a Point of Reaonance for Systems of Nonlinear Balance Laws

Pages: 279 – 294

DOI: http://dx.doi.org/10.4310/MAA.2003.v10.n2.a7

Authors

John Hong

Blake Temple

Abstract

We describe the generic solution of the Riemann problem near a point of resonance in a general 2x2 system of balance laws coupled to a stationary source. The source is treated as a conserved quantity in an augmented 3x3 system, and Resonance is between a nonlinear wave family and the stationary source. Transonic compressible Euler flow in a variable area duct, as well as spherically symmetric flow, are shown to be special cases of the general class of equations studied here.

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