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  "body": "\n## Summary\n\nIn a [[singular perturbation|G6J21TGRMM]] problem, a boundary layer is a thin region next to the boundary where the solution changes rapidly.\nOutside the layer, the solution of the reduced problem is a good approximation; inside it, this approximation fails.\nThe layer thickness tends to $0$ with the small parameter.\nThe notion comes from fluid dynamics, where Prandtl introduced it for the thin layer of fluid near a wall in which viscosity matters.\n\n## Explanations\n\n### L1 human\n\nAir flowing past a wing moves almost freely, except in a very thin sheet close to the surface where it is slowed down to rest.\nThat sheet is a boundary layer.\nTake the equation $\\varepsilon y'' + y' = 0$ with $y(0) = 0$ and $y(1) = 1$.\nIts solution is close to $1$ on most of the interval, but it falls to $0$ in a region of width about $\\varepsilon$ next to $x = 0$.\nAs $\\varepsilon$ gets smaller, the layer gets thinner and steeper.\n",
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