Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The fundamental solution of a conservation law without convexity

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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Additional Information

Youngsoo Ha
Affiliation: Department of Mathematical Sciences, Seoul National University, Gwanakro 1, Gwanak-Gu, Seoul 151-747, Republic of Korea
Email: youngamath.ha@gmail.com

Yong-Jung Kim
Affiliation: National Institute of Mathematical Sciences, Daejeon 305-811, Republic of Korea, and Department of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of Korea
Email: yongkim@kaist.edu

DOI: https://doi.org/10.1090/qam/1397
Received by editor(s): January 19, 2014
Published electronically: September 11, 2015
Additional Notes: This work was supported by the National Institute of Mathematical Sciences and the National Research Foundation of Korea (NRF-2014M1A7A1A03029872).
Article copyright: © Copyright 2015 Brown University

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