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Exact Solutions of a Mathematical Model for Fluid Transport in Peritoneal Dialysis

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Abstract

A mathematical model for fluid transport in peritoneal dialysis is constructed. The model is based on a nonlinear system of two-dimensional partial differential equations with corresponding boundary and initial conditions. Using the classical Lie scheme, we establish that the base system of partial differential equations (under some restrictions on coefficients) is invariant under the infinite-dimensional Lie algebra, which enables us to construct families of exact solutions. Moreover, exact solutions with a more general structure are found using another (non-Lie) technique. Finally, it is shown that some of the solutions obtained describe the hydrostatic pressure and the glucose concentration in peritoneal dialysis.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    R. Cherniha

  2. Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland

    J. Waniewski

Authors
  1. R. Cherniha
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  2. J. Waniewski
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1112–1119, August, 2005.

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Cherniha, R., Waniewski, J. Exact Solutions of a Mathematical Model for Fluid Transport in Peritoneal Dialysis. Ukr Math J 57, 1316–1324 (2005). https://doi.org/10.1007/s11253-005-0263-y

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  • DOI: https://doi.org/10.1007/s11253-005-0263-y

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