A steady-state convection-diffusion problem with a small diffusion of order O(epsilon) is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter O(epsilon), where epsilon is a small parameter. Using multiscale analysis, the asymptotic expansion for the solution is constructed and justified. The asymptotic estimates in the norm of Sobolev space H-1 as well as in the uniform norm are proved for the difference between the solution and proposed approximations with a predetermined accuracy with respect to the degree of epsilon.
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