@article {MATHEDUC.05995784,
author = {O'Brien, S.B.G.},
title = {Lin \& Segel's standing gradient problem revisited: A lesson in mathematical modeling and asymptotics.},
year = {2011},
journal = {SIAM Review},
volume = {53},
number = {4},
issn = {0036-1445},
pages = {775-796},
publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA},
doi = {10.1137/100794274},
abstract = {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 (Ume{\aa})},
msc2010 = {M65xx},
identifier = {2012c.00713},
}