Well-Posedness Theory for Hyperbolic Systems of Conservation Laws

  • Tai-Ping Liu
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 47)


The purpose of these lectures is to outline the main analytical ideas for the well-posedness theory based on nonlinear functionals. The first lecture gives a simple proof of theL- 1 contractionsemigroup property and introduces the Liu—Yang generalized entropy funtional for the scalar conservation law. Glimm’s interaction estimates and nonlinear functional for a general system are described in the second lecture. The third lecture illustrates the notion of wave tracing. The final lecture presents the L1-well posedness theory through the entropy functional. These lectures give an informal, intuitive presentation of the paper [1] of Tong Yang and the author.

The reader is also referred to this paper for the history of and references to the subject.


Shock Wave Generalize Entropy Rarefaction Wave Wave Pattern Riemann Problem 
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  1. 1.
    T.-P. Liu and T. Yang, Well-posedness theory for hyperbolic conservation lawsComm. Pure Appl. Math.52(1999), 1553–1586.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Tai-Ping Liu
    • 1
  1. 1.Academia SinicaInstitute of MathematicsTaipeiTaiwan

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