Riemann problems for nonstrictly hyperbolic systems of conservation laws

Authors:
David G. Schaeffer and Michael Shearer

Journal:
Trans. Amer. Math. Soc. **304** (1987), 267-306

MSC:
Primary 35L65; Secondary 35L67, 58C27

DOI:
https://doi.org/10.1090/S0002-9947-1987-0906816-5

MathSciNet review:
906816

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Abstract: The Riemann problem is solved for systems of hyperbolic conservation laws having quadratic flux functions. Equations with quadratic flux functions arise from neglecting higher order nonlinear terms in hyperbolic systems that fail to be strictly hyperbolic everywhere. Such equations divide into four classes, three of which are considered in this paper. The solution of the Riemann problem is complicated, with new types of shock waves, and new singularities in the dependence of the solution on the initial data. Several ideas are introduced to help organize and clarify the new phenomena.

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DOI:
https://doi.org/10.1090/S0002-9947-1987-0906816-5

Article copyright:
© Copyright 1987
American Mathematical Society