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Traveling-Wave Solutions for Hyperbolic Systems of Balance Laws

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • A. Dressel

    (University of Stuttgart, Department of Mathematics)

  • W. A. Yong

    (Tsinghua University, Zhou Pei-Yuan Center for Applied Mathematics)

Abstract

This report is concerned with the existence of traveling-wave solutions for hyperbolic systems of balance laws satisfying a stability condition and a Kawashima-like condition. We focus on the case where the traveling-wave equations have a singularity. The basic idea is to understand the singular equations as a three-scale multidimensional connection problem. Based on this understanding, we make two center manifold reductions to convert the problem to a one-dimensional problem, for which there is a well-known criterion for existence. The main technical issue is to show the effectiveness of the reductions under the aforesaid structural conditions. We also show how to generalize the results in [2] to more general singularities.

Suggested Citation

  • A. Dressel & W. A. Yong, 2008. "Traveling-Wave Solutions for Hyperbolic Systems of Balance Laws," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 485-492, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_46
    DOI: 10.1007/978-3-540-75712-2_46
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