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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Comparison principles for self-similar potential flow


Authors: Gui-Qiang G. Chen and Mikhail Feldman
Journal: Proc. Amer. Math. Soc. 140 (2012), 651-663
MSC (2010): Primary 35B51, 76N15, 76G25, 35Q35, 35J62, 35L65
Published electronically: June 21, 2011
MathSciNet review: 2846335
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish a strong comparison principle, as well as a weak comparison principle and a Hopf-type lemma, for elliptic solutions of the self-similar potential flow equation. A major difference from the steady case is that the coefficients of the equation depend on the potential function itself, as well as its gradient. We employ the divergence structure and other features of the equation to derive the results.


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Additional Information

Gui-Qiang G. Chen
Affiliation: Mathematical Institute, University of Oxford, Oxford, OX1 3LB, United Kingdom – and – Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: chengq@maths.ox.ac.uk

Mikhail Feldman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
Email: feldman@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10937-7
PII: S 0002-9939(2011)10937-7
Keywords: Comparison principle, Hopf-type lemma, maximum principle, self-similar, potential flow, velocity potential, divergence structure
Received by editor(s): April 26, 2010
Received by editor(s) in revised form: December 4, 2010
Published electronically: June 21, 2011
Communicated by: Walter Craig
Article copyright: © Copyright 2011 American Mathematical Society