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

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.