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Lin \& Segel’s standing gradient problem revisited: A lesson in mathematical modeling and asymptotics. (English)
SIAM Rev. 53, No. 4, 775-796 (2011).
In this very nice paper, a particular model from the textbook by [{\it C. C. Lin} and {\it L. A. Segel}, Mathematics applied to deterministic problems in the natural sciences. Classics in Applied Mathematics, 1. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. (1988; Zbl 0664.00026)] is revisited. The problem is associated with a standing gradient flow in physiology and has been picked as “an excellent didactic example which deserves a reappraisal.” Using a more informative nondimensionalization, the author demonstrates that the problem can be treated as a singular perturbation problem and, thanks to an alternative scaling procedure, the essential mechanism of the process is captured in a simple leading order solution. Several fundamental modeling techniques are skillfully reviewed in the paper; they may be adopted for the analysis of other problems arising in applied mathematics including, for instance, a model for absorption of nutrients into the roofs of a plant.
Reviewer: Svitlana P. Rogovchenko (Umeå)
Classification: M65
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