Abstract
The study of Singular Perturbation Problems (SPP) in dimension one has a great importance since the boundary layer problems are generally one-dimensional problems in the direction normal to the boundary and, as we will see throughout the chapters of this book, many higher dimensional problems (in terms of singular perturbations) will be reduced to solving some Ordinary Differential Equations (ODE) in dimension 1.
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- 1.
See Figure 1.2 for the asymptotic behavior of θ ɛ with respect to some small values of ɛ; since the corrector depends on the limit solution u 0, we consider the particular case where f(1) = 0.
References
M. Hamouda. Non-classical boundary layers for fourth-order equations with singular limit solution. Journal of Differential Integral Equations., Vol. 15, no. 12, 2002, 1435–1458.
M. Hamouda. Interior Layers for Second-Order Singular Equations. Applicable Analysis. Vol 81 (2002), no. 4, pp 837–866.
O’Riordan, E.; Quinn, J. A linearised singularly perturbed convection-diffusion problem with an interior layer. Appl. Numer. Math., 98 (2015), 1–17.
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Gie, GM., Hamouda, M., Jung, CY., Temam, R.M. (2018). Singular Perturbations in Dimension One. In: Singular Perturbations and Boundary Layers. Applied Mathematical Sciences, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-00638-9_1
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