| Abstract: | In this paper, we carry out a detailed analysis of the signaling and initial value problems associated with a general scalar conservation law that admits spatial variation in the flux function. The approach adopted here is to introduce a nonlinear phase variable directly into the problem and carry out the analysis in the space and phase variables rather than in space-time. This facilitates our efforts to create, through a bifurcation analysis, a clear picture of the process by which a smooth wave breaks to generate a propagating shock wave. |
