Mixed boundary condition

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Green: Neumann boundary condition; purple: Dirichlet boundary condition.
Green: Neumann boundary condition; purple: Dirichlet 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 Ω with piecewise-smooth boundary \partial \Omega, and \partial \Omega is divided into two parts, Γ1 and Γ2, one can use a Dirichlet boundary condition on Γ1 and a Neumann boundary condition on Γ2,

u_{\big| \Gamma_1} = u_0
\frac{\partial u}{\partial n}\bigg|_{\Gamma_2} = g

where u0 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.

[edit] See also

[edit] References

  • Guru, Bhag S.; Hiziroglu, Hüseyin R. (2004). Electromagnetic field theory fundamentals, 2nd ed.. Cambridge, UK; New York: Cambridge University Press, 593. ISBN 0521830168. 
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