Robin boundary condition

In mathematics, the Robin boundary condition (/ˈrɒbɪn/; properly French: ), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. In mathematics, the Robin boundary condition (/ˈrɒbɪn/; properly French: ), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Robin boundary conditions are a weighted combination of Dirichlet boundary conditions and Neumann boundary conditions. This contrasts to mixed boundary conditions, which are boundary conditions of different types specified on different subsets of the boundary. Robin boundary conditions are also called impedance boundary conditions, from their application in electromagnetic problems, or convective boundary conditions, from their application in heat transfer problems (Hahn, 2012). If Ω is the domain on which the given equation is to be solved and ∂Ω denotes its boundary, the Robin boundary condition is: for some non-zero constants a and b and a given function g defined on ∂Ω. Here, u is the unknown solution defined on Ω and ∂u/∂n denotes the normal derivative at the boundary. More generally, a and b are allowed to be (given) functions, rather than constants.