Traveling-Wave Solutions for Hyperbolic Systems of Balance Laws

A. Dressel () and W. A. Yong ()
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A. Dressel: University of Stuttgart, Department of Mathematics
W. A. Yong: Tsinghua University, Zhou Pei-Yuan Center for Applied Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 485-492 from Springer

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.

Keywords: Hyperbolic System; Extended Thermodynamic; Center Manifold Reduction; Connection Problem; Discrete Boltzmann Equation (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_46

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DOI: 10.1007/978-3-540-75712-2_46

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