Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach

Ijioma, Ekeoma; Muntean, Adrian

doi:10.1090/qam/1509

Online ISSN 1552-4485; Print ISSN 0033-569X

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Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach

Authors: Ekeoma R. Ijioma and Adrian Muntean
Journal: Quart. Appl. Math. 77 (2019), 71-104
MSC (2010): Primary 80A32, 76M50; Secondary 80A25, 35B27
DOI: https://doi.org/10.1090/qam/1509
Published electronically: June 19, 2018
MathSciNet review: 3897920
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Abstract | References | Similar Articles | Additional Information

Abstract: We target the periodic homogenization of a semi-linear reaction-diffusion-convection system describing filtration combustion, where fast drifts are triggered by the competition between heat and mass transfer processes in an asymptotic regime of dominant convection. In addition, we consider the interplay between surface nonlinear chemical reactions and transport processes. To handle the oscillations occurring due to the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain, for suitably scaled model parameters, the upscaled system of equations together with effective transport parameters. The main difficulty is to treat the case of a coupled multi-physics problem. We proceed by extending the results reported by G. Allaire et al. and other related papers in this context to the case of a coupled system of evolution equations pertinent to filtration combustion.

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