NONMONOTONICITY OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS OCCURRING IN THE THEORY OF URINE FORMATION.
MARYLAND UNIV COLLEGE PARK INST FOR FLUID DYNAMICS AND APPLIED MATHEMATICS
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A model is given for the renal medulla which leads to a functional boundary value problem for a fourth order system of linear differential equations c prime G c, where G is a piecewise constant 4 X 4 matrix and the components of c represent solute concentrations in uriniferous tubules and in blood vessels. c1 and c3 are specified at x o, and c P c at x lambda lambda is the length of the medulla where P is a permutation matrix whose main diagonal is zero. Solutions are sought that are continuous and piecewise differentiable. Existence uniqueness, and positiveness of c are shown. Certain arithmatic averages of the components of c correspond to the interstitial solute concentration. Under the assumption that active solute transport is limited to that part of the model corresponding to the outer medulla, which leads to certain restrictions on the matrix G, it is shown that the interstitial concentration is nonmonotonic and achieves its maximum value in the outer medulla - a result of interest in the theory of urine formation. Author