Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Spherical, cylindrical and one-dimensional gas flows

Author: J. B. Keller
Journal: Quart. Appl. Math. 14 (1956), 171-184
MSC: Primary 76.0X
DOI: https://doi.org/10.1090/qam/80481
MathSciNet review: 80481
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Abstract: The problem of spherical, cylindrical or planar flow of a polutropic gas has been formulated in Lagrangian variables, giving rise to a non-linear second order partial differential equation in two variables, $ h$ and $ t$. A class of special solutions of this equation has been found by separation of variables, and these solutions depend upon an arbitrary function which is related to the arbitrary entropy distribution in the gas. By specializing this function solutions corresponding to the expansion into a vacuum of an isentropic or non-isentropic gas cloud have been obtained as well as solutions corresponding to the propagation of finite and of strong shocks in variable media.

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DOI: https://doi.org/10.1090/qam/80481
Article copyright: © Copyright 1956 American Mathematical Society

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