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| [[File:Mixed boundary conditions.svg|right|thumb|Green: Neumann boundary condition; purple: Dirichlet boundary condition.]]
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| In [[mathematics]], a '''mixed boundary condition''' for a [[partial differential equation]] indicates that different [[boundary condition]]s are used on different parts of the [[boundary (topology)|boundary]] of the [[domain (mathematics)|domain]] of the equation.
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| For example, if ''u'' is a solution to a partial differential equation on a set <math>\Omega</math> with [[piecewise]]-[[smooth function|smooth]] boundary <math>\partial\Omega</math>, and <math>\partial\Omega</math> is divided into two parts, <math>\Gamma_1</math> and <math>\Gamma_2</math>, one can use a [[Dirichlet boundary condition]] on <math>\Gamma_1</math> and a [[Neumann boundary condition]] on <math>\Gamma_2</math>:
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| : <math>u_{\big| \Gamma_1} = u_0</math>
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| : <math>\left. \frac{\partial u}{\partial n}\right|_{\Gamma_2} = g</math>
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| where ''u₀'' and ''g'' are given functions defined on those portions of the boundary.
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| [[Robin boundary condition]] is another type of hybrid boundary condition; it is a [[linear combination]] of Dirichlet and Neumann boundary conditions.
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| ==See also==
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| *[[Dirichlet boundary condition]]
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| *[[Neumann boundary condition]]
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| *[[Cauchy boundary condition]]
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| *[[Robin boundary condition]]
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| ==References==
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| *{{cite book
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| | last = Guru
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| | first = Bhag S.
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| | coauthors = Hızıroğlu, Hüseyin R.
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| | title = Electromagnetic field theory fundamentals, 2nd ed.
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| | publisher = Cambridge, UK; New York: Cambridge University Press
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| | date = 2004
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| | isbn = 0-521-83016-8
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| | page = 593
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| }}
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| {{Mathapplied-stub}}
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| [[Category:Boundary conditions]]
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| [[Category:Partial differential equations]]
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