Asymptotic expansions for transport problems in thin graph-like networks
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.
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.