Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Conserving the wrong variables in gas dynamics: A Riemann solution with singular shocks


Authors: Barbara Lee Keyfitz and Charis Tsikkou
Journal: Quart. Appl. Math. 70 (2012), 407-436
MSC (2010): Primary 35L65, 35L67; Secondary 34E15, 34C37
DOI: https://doi.org/10.1090/S0033-569X-2012-01317-1
Published electronically: May 16, 2012
MathSciNet review: 2986129
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a system of two equations derived from isentropic gas dynamics with no classical Riemann solutions. We show existence of unbounded self-similar solutions (singular shocks) of the Dafermos regularization of the system. Our approach is based on the blowing-up approach of geometric singular perturbation theory.


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Additional Information

Barbara Lee Keyfitz
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Email: bkeyfitz@math.ohio-state.edu

Charis Tsikkou
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Email: tsikkou@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01317-1
Keywords: Conservation laws, singular shocks, Dafermos regularization, geometric singular perturbation theory, nonhyperbolicity, blow-up
Received by editor(s): February 14, 2012
Published electronically: May 16, 2012
Additional Notes: The first author was supported in part by NSF Grant DMS0807569 and by DOE Grant DE-SC0001285
The second author was supported in part by DOE Grant DE-SC0001285
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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