Abstract
Singular perturbations of partial differential equations (PDEs) are encountered due to the nature of certain physical models (e.g., small viscosity in Navier-Stokes equations), or to analyze some asymptotic limiting behavior (long time, long distances). In such cases, sometimes, certain usually nondimensional groups of terms are first identified, e.g., electron to ion mass ratio. Besides, singular perturbations are encountered for regularization purposes, e.g., in the numerical treatment of hyperbolic or ultraparabolic PDEs, like the Fokker-Planck equation, through parabolic regularization.
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Akhmetov, D.R., Jr., M.M.L., Spigler, R. (2010). Singular Perturbations of Parabolic Equations With or Without Boundary Layers. In: Fitt, A., Norbury, J., Ockendon, H., Wilson, E. (eds) Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry(), vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12110-4_10
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DOI: https://doi.org/10.1007/978-3-642-12110-4_10
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