Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Existence of turning points for the response diagram of the Poiseuille flow with prescribed flow-rate

Author: Giovanni Cimatti
Journal: Quart. Appl. Math. 65 (2007), 523-528
MSC (2000): Primary 76D03, 76D05
DOI: https://doi.org/10.1090/S0033-569X-07-01058-1
Published electronically: June 6, 2007
MathSciNet review: 2354885
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Abstract: We study the stationary Poiseuille flow in a cylindrical channel of arbitrary cross-section with temperature dependent viscosity and internal dissipation. We assume the flow-rate $ \Phi$ given and the axial pressure gradient $ \mu$ unknown. This leads to a non-local problem. We show the existence in the response diagram, the plane $ (\Phi,\mu)$, of two turning points.

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Giovanni Cimatti
Affiliation: Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, Italy
Email: cimatti@dm.unipi.it

DOI: https://doi.org/10.1090/S0033-569X-07-01058-1
Keywords: Poiseuille flow, temperature dependent viscosity, existence and uniqueness of solutions.
Received by editor(s): September 28, 2006
Published electronically: June 6, 2007
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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