Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#287285] of Harold Layton

Papers Published

  1. Layton, HE, Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism, Mathematical Biosciences, vol. 84 no. 2 (1987), pp. 197-210, ISSN 0025-5564
    (last updated on 2017/12/12)

    This paper establishes some results for the existence and uniqueness of solutions to a previously published mathematical model of the mammalian urine concentrating mechanism [H.E. Layton, Distribution of Henle's loops may enhance urine concentrating capability, Biophys. J. 49:1033-1040 (1986)]. In particular, the contraction mapping principle is used to show that for sufficiently small and sufficiently large values of a positive parameter β there exist unique solutions to the model, whether it be endowed with first-order kinetics or Michaelis-Menten kinetics. Large or small β corresponds to large or small rates of active transport of NaCl from the ascending limbs. The Schauder principle is used to show that there exist solutions to the model for physiologically reasonable reabsorption kinetics, including first-order and Michaelis-Menten kinetics for all values of β. © 1987.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320