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.
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Dressel, A., Yong, W.A. (2008). Traveling-Wave Solutions for Hyperbolic Systems of Balance Laws. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_46
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DOI: https://doi.org/10.1007/978-3-540-75712-2_46
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