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Admissibility Criteria and Admissible Weak Solutions of Riemann Problems for Conservation Laws of Mixed Type: A Summary

  • L. Hsiao
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 27)

Abstract

Consider the model system
$$ \left\{ {\begin{array}{*{20}{c}} {{v_t} + p{{(u)}_x} = 0} \\ {{u_t} - {v_x} = 0} \\ \end{array} } \right. $$
(1.1)
which describes the one-dimensional isothermal motion of a compressible elastic fluid or solid in Lagrangian coordinate system. Here v denotes the velocity, u the specific volume for a fluid or displacement gradient for a solid, and -p is the stress which is determined through a constitutive relation.

Keywords

Mixed Type Hyperbolic System Riemann Problem Displacement Gradient Shock Wave Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • L. Hsiao
    • 1
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institute of MathematicsAcademia SinicaBeijingP.R. China

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