Opuscula Math. 43, no. 2 (2023), 199-220
https://doi.org/10.7494/OpMath.2023.43.2.199

Opuscula Mathematica

Fernando A. Morales

Abstract. We present the asymptotic analysis of the steady advection-diffusion equation in a thin tube. The problem is modeled in a mixed-type variational formulation, in order to separate the phenomenon in the axial direction and a transverse one. Such formulation makes visible the natural separation of scales within the problem and permits a successful asymptotic analysis, delivering a limiting form, free from the initial geometric singularity and suitable for approximating the original one. Furthermore, it is shown that the limiting problem can be simplified to a significantly simpler structure.

Keywords: asymptotic analysis, mixed-type variational formulations, advection-diffusion.

Mathematics Subject Classification: 80A20, 35F15.

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• Fernando A. Morales
• https://orcid.org/0000-0002-5691-1247
• Universidad Nacional de Colombia, Sede Medellín, Escuela de Matemáticas, Carrera 65 # 59A-110, Bloque 43, of 106, Medellín - Colombia
• Communicated by P.A. Cojuhari.
• Revised: 2023-02-20.
• Accepted: 2023-02-21.
• Published online: 2023-03-27.