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Existence and uniqueness of solutions in general multisolute renal flow problems

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Abstract

This paper considers systems of differential equations that describe flows in renal networks. The flow geometry is of the type that occurs in modelling the renal medulla. The unknowns in the system include the flow rate, the hydrostatic pressure, and the concentrations of the various solutes. Existence and uniqueness of solutions of the appropriate boundary value problems are established, in the case of small permeability coefficients and transport rates, or large diffusion coefficients and small resistance to flow constants.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Mississippi State University, 39762, Mississippi State, MS, USA

    J. B. Garner

  2. Institute for Physical Science and Technology, The University of Maryland, 20742, College Park, MD, USA

    R. B. Kellogg

Authors
  1. J. B. Garner
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  2. R. B. Kellogg
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Additional information

Work supported in part by NIH Grants 5-R01-AM28617 and 7-R01-DK38817

Work supported in part by NIH Grant 5-R01-AM20373

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Garner, J.B., Kellogg, R.B. Existence and uniqueness of solutions in general multisolute renal flow problems. J. Math. Biology 26, 455–464 (1988). https://doi.org/10.1007/BF00276373

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  • DOI: https://doi.org/10.1007/BF00276373

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