Asymptotics of diffusion-limited fast reactions

Seidman, Thomas; Muntean, Adrian

doi:10.1090/qam/1496

Authors: Thomas I. Seidman and Adrian Muntean
Journal: Quart. Appl. Math. 76 (2018), 199-213
MSC (2010): Primary 35K57, 35R37
DOI: https://doi.org/10.1090/qam/1496
Published electronically: November 20, 2017
MathSciNet review: 3769894
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Abstract: We are concerned with the fast-reaction asymptotics $\lambda \to \infty$ for a semi-linear coupled diffusion-limited reaction system in contact with infinite reservoirs of reactants. We derive the system of limit equations and prove the uniqueness of its solutions for equal diffusion coefficients. Additionally, we emphasize the structure of the limit free boundary problem. The key tools of our analysis include (uniform with respect to $\lambda$) $L^1$-estimates for both fluxes and products of reaction and a balanced formulation, where combinations of the original components which balance the fast reaction are used.

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