Existence of Traveling-Wave Solutions for Hyperbolic Systems of Balance Laws

This paper is concerned with traveling-wave solutions for hyperbolic systems of balance laws satisfying a stability condition and a Kawashima-like condition. We are interested in the case where the traveling-wave equations have a singularity, which is absent for 2 × 2 systems satisfying the two conditions. To deal with the singularity, we reduce the problem to a parametrized one without singularity by using the center manifold theorem. For the parametrized problem, we prove the existence of solutions by modifying an existing argument in the literature. In this way, we show the existence of traveling-wave solutions.