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

Entropy 

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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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