Existence and stability of traveling wave solutions to one-sided mixed initial-boundary value problem for first-order quasilinear hyperbolic systems

When one characteristic of the system is linearly degenerate, under suitable boundary conditions, we get the existence of traveling wave solutions located on the corresponding characteristic trajectory to the one‐sided mixed initial‐boundary value problem. When the system is linearly degenerate, by introducing the semi‐global normalized coordinates, we derive the related formulas of wave decomposition to prove the stability of traveling wave solutions corresponding to all leftward and the rightmost characteristic trajectories. Finally, for the traveling wave solutions corresponding to other rightward characteristic trajectories, some examples show their possible instability. Copyright © 2014 John Wiley & Sons, Ltd.