Robin boundary condition

In mathematics, the Robin boundary condition (/ˈrɒbɪn/ ROB-in, French: [ʁɔbɛ̃]), or third-type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). It is used when solving partial differential equations and ordinary differential equations.

The Robin boundary condition specifies a linear combination of the value of a function and the value of its derivative at the boundary of a given domain. It is a generalization of the Dirichlet boundary condition, which specifies only the function's value, and the Neumann boundary condition, which specifies only the function's derivative. A common physical example is in heat transfer, where a surface might lose heat to the environment via convection. The rate of heat flow (related to the derivative of temperature) would be proportional to the difference between the surface temperature (the value of the temperature function) and the ambient temperature.

Other equivalent names in use are Fourier-type condition and radiation condition.

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