Abstract
In this chapter, we will study the extension of the results on singular perturbations to higher dimensions. In dimension d ≥ 2, new problems arise related to the geometry of the domain, and in particular whether the domain is sufficiently regular or it has corners. Even if the domain is smooth, some boundary layers occur which are due to the curvature of the boundary. These issues necessitating some elements of geometry are addressed in Chapters 3 and 5 The case of a domain with corners is particularly complicated and some aspects of it will be studied in Chapter 4; this includes the possible lack of regularity of the inviscid solution and the appearance of the so-called corner boundary layers due to the interaction between the boundary layers that meet at a corner.
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References
Chang-Yeol Jung and Roger Temam. On parabolic boundary layers for convection-diffusion equations in a channel: analysis and numerical applications. J. Sci. Comput., 28(2–3):361–410, 2006.
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Gie, GM., Hamouda, M., Jung, CY., Temam, R.M. (2018). Singular Perturbations in Higher Dimensions in a Channel. In: Singular Perturbations and Boundary Layers. Applied Mathematical Sciences, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-00638-9_2
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DOI: https://doi.org/10.1007/978-3-030-00638-9_2
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Online ISBN: 978-3-030-00638-9
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