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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Incompressible reacting flows


Author: Joel D. Avrin
Journal: Trans. Amer. Math. Soc. 349 (1997), 3875-3892
MSC (1991): Primary 35B40, 35K55, 35K57, 35Q10, 80A25
MathSciNet review: 1422594
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish steady-state convergence results for a system of
reaction-convection-diffusion equations that model in particular combustion phenomena in the presence of nontrivial incompressible fluid motion. Despite the presence of the convection terms, we find that the asymptotic behavior of the system is identical to the case we have previously considered in which the velocity field was set equal to zero. In particular we are again able to establish the convergence of solutions to steady-states and to explicitly calculate the steady-states from the initial and boundary data. Key to our analysis is the establishment of high-order uniform bounds on the temperature and mass fraction components, a process significantly complicated by the presence of the convection terms.


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Additional Information

Joel D. Avrin
Affiliation: Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223
Email: fma00jda@unccvm.uncc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01945-4
PII: S 0002-9947(97)01945-4
Received by editor(s): September 20, 1994
Article copyright: © Copyright 1997 American Mathematical Society