Opuscula Math. 43, no. 2 (2023), 199-220

Opuscula Mathematica

Asymptotic analysis of the steady advection-diffusion problem in axial domains

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
  • ORCID iD 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.
  • Received: 2023-01-24.
  • Revised: 2023-02-20.
  • Accepted: 2023-02-21.
  • Published online: 2023-03-27.
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Cite this article as:
Fernando A. Morales, Asymptotic analysis of the steady advection-diffusion problem in axial domains, Opuscula Math. 43, no. 2 (2023), 199-220, https://doi.org/10.7494/OpMath.2023.43.2.199

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