Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

Incompressible reacting flows

Author(s): 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: 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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