The signaling problem for a system of conservation laws in a single space variable is treated through the deployment of a perturbation analysis. Our method of approach involves the direct use of two nonlinear phase variables making possible the study of weakly nonlinear interacting waves arising from a boundary disturbance consisting of two wave modes. As a result of our analysis, the asymptotic solution is derived, and the class of admissible boundary disturbances is distinguished as well. An application is then made to gas dynamics in one space dimension to investigate the propagation and interaction of two sound waves for which the base state is taken to be a steady supersonic flow.
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