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Scalar Conservation Laws and Spatially Dependent Flux Functions
Author(s) -
He Yuanping,
Moodie T. Bryant
Publication year - 1994
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1994913215
Subject(s) - conservation law , scalar (mathematics) , mathematical analysis , nonlinear system , phase space , mathematics , bifurcation , shock wave , shock (circulatory) , carry (investment) , classical mechanics , statistical physics , physics , mechanics , geometry , medicine , finance , quantum mechanics , economics , thermodynamics
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.