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  "body": "\n## Summary\n\nA problem with a small parameter $\\varepsilon$ is singularly perturbed when setting $\\varepsilon = 0$ does not give a uniformly good approximation of its solutions.\nA typical cause is a small parameter in front of the highest derivative.\nThen the reduced equation has lower order and cannot meet all boundary or initial conditions.\nThe solutions then change rapidly in thin regions, such as boundary layers.\nSingular perturbations appear in fluid flow at high Reynolds number, chemical kinetics and slow-fast systems.\n\n## Explanations\n\n### L1 human\n\nSometimes a tiny term in an equation can be dropped without much harm, and sometimes it cannot.\nIn $\\varepsilon y'' + y' = 0$ with $y(0) = 0$ and $y(1) = 1$, dropping $\\varepsilon y''$ leaves $y' = 0$, whose solutions are constants.\nA constant cannot be $0$ at one end and $1$ at the other.\nThe true solution is close to $1$ on most of the interval, but it drops steeply to $0$ in a thin layer near $x = 0$.\nThat thin layer is the mark of a singular perturbation.\n",
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