The fundamental solution of a conservation law without convexity

Ha, Youngsoo; Kim, Yong-Jung

doi:10.1090/qam/1397

Authors: Youngsoo Ha and Yong-Jung Kim
Journal: Quart. Appl. Math. 73 (2015), 661-678
MSC (2000): Primary 35L67, 35L65, 76L05
DOI: https://doi.org/10.1090/qam/1397
Published electronically: September 11, 2015
MathSciNet review: 3432277
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Abstract: The nonnegative fundamental solution of a scalar conservation law is constructed when its flux may have a finite number of inflection points. The constructed solution can be either explicit and implicit depending on the flux. This fundamental solution consists of a series of rarefaction waves, contact discontinuities and a shock. These analytically constructed fundamental solutions are also compared with numerical approximations, which possess the structure of the analytically constructed fundamental solution.

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