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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Incompressible reacting flows
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by Joel D. Avrin PDF
Trans. Amer. Math. Soc. 349 (1997), 3875-3892 Request permission

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
  • Received by editor(s): September 20, 1994
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 3875-3892
  • MSC (1991): Primary 35B40, 35K55, 35K57, 35Q10, 80A25
  • DOI: https://doi.org/10.1090/S0002-9947-97-01945-4
  • MathSciNet review: 1422594