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Scalar Conservation Laws and Spatially Dependent Flux Functions

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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.
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Document Type: Research Article

Affiliations: University of Alberta, Edmonton

Publication date: March 1, 1994

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