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Published By American Institute Of Mathematical Sciences

1556-181x

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Christian Budde ◽  
Marjeta Kramar Fijavž
Keyword(s):  

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Marta Marulli ◽  
Vuk Miliši$\grave{\rm{c}}$ ◽  
Nicolas Vauchelet

<p style='text-indent:20px;'>This work deals with a mathematical analysis of sodium's transport in a tubular architecture of a kidney nephron. The nephron is modelled by two counter-current tubules. Ionic exchange occurs at the interface between the tubules and the epithelium and between the epithelium and the surrounding environment (interstitium). From a mathematical point of view, this model consists of a 5<inline-formula><tex-math id="M1">\begin{document}$ \times $\end{document}</tex-math></inline-formula>5 semi-linear hyperbolic system. In literature similar models neglect the epithelial layers. In this paper, we show rigorously that such models may be obtained by assuming that the permeabilities between lumen and epithelium are large. We show that when these permeabilities grow, solutions of the 5<inline-formula><tex-math id="M2">\begin{document}$ \times $\end{document}</tex-math></inline-formula>5 system converge to those of a reduced 3<inline-formula><tex-math id="M3">\begin{document}$ \times $\end{document}</tex-math></inline-formula>3 system without epithelial layers. The problem is defined on a bounded spacial domain with initial and boundary data. In order to show convergence, we use <inline-formula><tex-math id="M4">\begin{document}$ {{{\rm{BV}}}} $\end{document}</tex-math></inline-formula> compactness, which leads to introduce initial layers and to handle carefully the presence of lateral boundaries. We then discretize both 5<inline-formula><tex-math id="M5">\begin{document}$ \times $\end{document}</tex-math></inline-formula>5 and 3<inline-formula><tex-math id="M6">\begin{document}$ \times $\end{document}</tex-math></inline-formula>3 systems, and show numerically the same asymptotic result, for a fixed meshsize.</p>


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sergei Avdonin ◽  
Julian Edward
Keyword(s):  

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giuseppe Maria Coclite ◽  
Nicola De Nitti ◽  
Mauro Garavello ◽  
Francesca Marcellini

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Leandro M. Del Pezzo ◽  
Nicolás Frevenza ◽  
Julio D. Rossi

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