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  "body": "\n## Summary\n\nA Robin boundary condition prescribes a linear combination of the value of the unknown function and its outward normal derivative on the boundary.\nIt interpolates between the [[Dirichlet condition|EETVA6QYX4]] and the [[Neumann condition|GS3KT2H645]].\nIt models heat exchange with the surroundings, where the flux through the wall is proportional to the temperature difference.\nThe separated boundary conditions of [[Sturm–Liouville theory|7WV6B2502K]] are of this type.\nSee the [[definition|Y19WM1EMS7]].\n\n## Explanations\n\n### L1 human\n\nThink of a hot rod whose ends lose heat to the air.\nThe heat flowing out of an end is proportional to how much hotter the end is than the air.\nThis links the slope of the temperature at the end to its value there.\nFor an end at $x = 1$ with outside temperature $0$, the condition reads $u'(1) = -h\\, u(1)$ for a constant $h \u003e 0$.\n",
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