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Incompressible reacting flows. (English) Zbl 0883.35012

Author’s summary: 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. The 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.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
80A25 Combustion
35Q35 PDEs in connection with fluid mechanics
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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