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Scalar Conservation Laws with Boundary Effect

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • Tao Pan

    (Guangxi University, Dept. of Mathematics and Information Sciences
    Mie University, Lab. of Bioinformation and Food Engineering, Faculty of Bioresources)

  • Hongxia Liu

    (Jinan University, Dept. of Mathematics)

Abstract

This paper reviews the recent work on the global weak entropy solutions of scalar conservation laws with boundary effect and the global error estimate for viscosity methods to initial-boundary value problems of scalar conservation laws. In section 2, we state how to obtain the existence of weak entropy solution for general nonconvex scalar conservation laws by Dafermos’s polygonal approximations method which can be used to simulate geometric structure of the weak entropy solution. We also state the large time behaviors of weak entropy solution by discussing the interaction of elementary waves for scalar convex conservation laws on a bounded domain. In section 3, we are concerned with the global error estimate for viscous approximations to inviscid solution to initial-boundary value problems of convex scalar conservation laws by the matching traveling wave solutions method.

Suggested Citation

  • Tao Pan & Hongxia Liu, 2003. "Scalar Conservation Laws with Boundary Effect," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 775-787, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_73
    DOI: 10.1007/978-3-642-55711-8_73
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