What is it about?

A rigorous asymptotic method is proposed to construct complete asymptotic expansion for the solution of a convection-dominated transport problems in thin graph-like network with a strong intensity of physical processes on the boundary.

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Why is it important?

Three-dimensional numerical calculations for models of various complex processes associated with flow and transport in thin networks don't provide an acceptable level of accuracy. Another approach is to use reduction techniques to obtain simplified models of lower dimensions. However, in many cases, these reductions are the result of significant simplifications and assumptions that do not correspond to real processes and are not strictly justified. Therefore, it is crucial to develop rigorous asymptotic methods for solving transport problems in thin three-dimensional networks.


I hope this article and method proposed there will be useful for other applied problems in thin networks that are prototypes of biological neural networks, blood vessels, networks of cracks, and so on.

Taras Melnyk
Institute of Applied Analysis and Numerical Simulation

Read the Original

This page is a summary of: Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: Strong boundary interactions, Asymptotic Analysis, March 2024, IOS Press,
DOI: 10.3233/asy-231876.
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