Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A self-similar viscosity approach for the Riemann problem in isentropic gas dynamics and the structure of the solutions

Author: Yong Jung Kim
Journal: Quart. Appl. Math. 59 (2001), 637-665
MSC: Primary 35L65; Secondary 35L67, 76N10, 76N15
DOI: https://doi.org/10.1090/qam/1866552
MathSciNet review: MR1866552
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Abstract: We study the Riemann problem for the system of conservation laws of one-dimensional isentropic gas dynamics in Eulerian coordinates. We construct solutions of the Riemann problem by the method of self-similar zero-viscosity limits, where the self-similar viscosity only appears in the equation for the conservation of momentum. No size restrictions on the data are imposed. The structure of the solutions obtained is also analyzed.

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DOI: https://doi.org/10.1090/qam/1866552
Article copyright: © Copyright 2001 American Mathematical Society

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