Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Asymptotics of diffusion-limited fast reactions

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
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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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Additional Information

Thomas I. Seidman
Affiliation: Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland 21250
Email: seidman@umbc.edu

Adrian Muntean
Affiliation: Department of Mathematics and Computer Science, Karlstad University, Sweden
Email: adrian.muntean@kau.se

DOI: https://doi.org/10.1090/qam/1496
Keywords: Asymptotics, fast reaction, energy method, compactness, reaction-diffusion systems
Received by editor(s): April 4, 2016
Published electronically: November 20, 2017
Article copyright: © Copyright 2017 Brown University

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