## Comparison principles for self-similar potential flow

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- by Gui-Qiang G. Chen and Mikhail Feldman PDF
- Proc. Amer. Math. Soc.
**140**(2012), 651-663 Request permission

## 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.## References

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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
- MR Author ID: 249262
- ORCID: 0000-0001-5146-3839
- Email: chengq@maths.ox.ac.uk
**Mikhail Feldman**- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
- MR Author ID: 226925
- Email: feldman@math.wisc.edu
- 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
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**140**(2012), 651-663 - MSC (2010): Primary 35B51, 76N15, 76G25, 35Q35, 35J62, 35L65
- DOI: https://doi.org/10.1090/S0002-9939-2011-10937-7
- MathSciNet review: 2846335