Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Existence of optimal shape for a system of conservation laws in a free air-porous domain


Author: Arian Novruzi
Journal: Quart. Appl. Math. 64 (2006), 641-661
MSC (2000): Primary 49J20, 93C20, 76D05, 76D06
Published electronically: November 15, 2006
MathSciNet review: 2284464
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Abstract: We consider a shape optimization problem related to a nonlinear system of PDE describing the gas dynamics in a free air-porous domain, including gas concentrations, temperature, velocity and pressure. The velocity and pressure are described by the Stokes and Darcy laws, while concentrations and temperature are given by mass and heat conservation laws. The system represents a simplified dry model of gas dynamics in the channel and graphite diffusive layers of hydrogen fuel cells. The model is coupled with the other part of the domain through some mixed boundary conditions, involving nonlinearities, and pressure boundary conditions. Under some assumptions we prove that the system has a solution and that there exists a channel domain in the class of Lipschitz domains minimizing a certain functional measuring the membrane temperature distribution, total current, water vapor transport and channel inlet/outlet pressure drop.


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Additional Information

Arian Novruzi
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Canada
Address at time of publication: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, ON, K1N 6N5, Canada
Email: novruzi@uottawa.ca

DOI: https://doi.org/10.1090/S0033-569X-06-01012-X
Received by editor(s): June 21, 2005
Published electronically: November 15, 2006
Additional Notes: This work was supported by NSERC Discovery Grants and by Ballard through the MITACS project Mathematical Modeling and Scientific Computation (MMSC)
Article copyright: © Copyright 2006 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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