Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The sonic line as a free boundary

Authors: Barbara Lee Keyfitz, Allen M. Tesdall, Kevin R. Payne and Nedyu I. Popivanov
Journal: Quart. Appl. Math. 71 (2013), 119-133
MSC (2010): Primary 35L65, 35M30, 76H05; Secondary 35R35, 42A38
DOI: https://doi.org/10.1090/S0033-569X-2012-01283-6
Published electronically: October 2, 2012
MathSciNet review: 3075538
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the steady transonic small disturbance equations on a domain and with data that lead to a solution that depends on a single variable. After writing down the solution, we show that it can also be found by using a hodograph transformation followed by a partial Fourier transform. This motivates considering perturbed problems that can be solved with the same technique. We identify a class of such problems.

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Additional Information

Barbara Lee Keyfitz
Affiliation: The Fields Institute, Toronto
Address at time of publication: Department of Mathematics, The Ohio State University
Email: bkeyfitz@math.ohio-state.edu

Allen M. Tesdall
Affiliation: Department of Mathematics, College of Staten Island, City University of New York
Email: allen.tesdall@csi.cuny.edu

Kevin R. Payne
Affiliation: Dipartimento di Matematica, Universita di Milano
Email: kevin.payne@unimi.it

Nedyu I. Popivanov
Affiliation: Department of Mathematics and Informatics, University of Sofia
Email: nedyu@fmi.uni-sofia.bg

DOI: https://doi.org/10.1090/S0033-569X-2012-01283-6
Received by editor(s): April 1, 2011
Published electronically: October 2, 2012
Additional Notes: The first author’s research was supported by NSERC of Canada, NSF and the Department of Energy. This project was started during a visit to Loughborough University, funded by the Maxwell Institute.
The second author’s research was supported by NSERC of Canada, NSF, Research Foundation of CUNY, the Fields Institute, and the Department of Energy.
The third author was supported by MIUR project “Equazioni alle derivate parziali e disuguaglianze funzionali: aspetti geometrici, proprietá qualitative e applicazioni”. Additional support from the Fields Institute is acknowledged.
The fourth author was partially supported by the Bulgarian NSF under Grant DO 02-115/2008 “Centre of Excellence on Supercomputer Applications (SuperCA)”. Support from The Ohio State University is acknowledged.
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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