Definitions

# Mixed boundary condition

In mathematics, a mixed boundary condition for a partial differential equation indicates that different boundary conditions are used on different parts of the boundary of the domain of the equation.

For example, if $u,$ is a solution to a partial differential equation on a set $Omega,$ with piecewise-smooth boundary $partial Omega,$ and $partial Omega$ is divided into two parts, $Gamma_1 ,$ and $Gamma_2,$ one can use a Dirichlet boundary condition on $Gamma_1,$ and a Neumann boundary condition on $Gamma_2,$,

$u_\left\{big| Gamma_1\right\} = u_0$

$frac\left\{partial u\right\}\left\{partial n\right\}bigg|_\left\{Gamma_2\right\} = g$

where $u_0,$ and $g,$ are given functions defined on those portions of the boundary.

Robin boundary condition is another type of hybrid boundary condition; it is a linear combination of Dirichlet and Neumann boundary conditions.