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- Robin_boundary_condition abstract "In mathematics, the Robin boundary condition (/ˈrɔːbɪn/; properly French: [ʁoˈbɛ̃]), 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.If Ω is the domain on which the given equation is to be solved and denotes its boundary, the Robin boundary condition is:for some non-zero constants a and b and a given function g defined on . Here, u is the unknown solution defined on and denotes the normal derivative at the boundary. More generally, a and b are allowed to be (given) functions, rather than constants.In one dimension, if, for example, , the Robin boundary condition becomes the conditions:notice the change of sign in front of the term involving a derivative: that is because the normal to at 0 points in the negative direction, while at 1 it points in the positive direction.Robin boundary conditions are commonly used in solving Sturm–Liouville problems which appear in many contexts in science and engineering.In addition, the Robin boundary condition is a general form of the insulating boundary condition for convection–diffusion equations. Here, the convective and diffusive fluxes at the boundary sum to zero:where D is the diffusive constant, u is the convective velocity at the boundary and c is the concentration. The second term is a result of Fick's law of diffusion.".
- Robin_boundary_condition wikiPageID "9945920".
- Robin_boundary_condition wikiPageRevisionID "580547643".
- Robin_boundary_condition hasPhotoCollection Robin_boundary_condition.
- Robin_boundary_condition subject Category:Boundary_conditions.
- Robin_boundary_condition type Abstraction100002137.
- Robin_boundary_condition type BoundaryCondition106755776.
- Robin_boundary_condition type BoundaryConditions.
- Robin_boundary_condition type Communication100033020.
- Robin_boundary_condition type Condition106755568.
- Robin_boundary_condition type Message106598915.
- Robin_boundary_condition type Postulate106753299.
- Robin_boundary_condition type Premise106753800.
- Robin_boundary_condition type Proposition106750804.
- Robin_boundary_condition type Statement106722453.
- Robin_boundary_condition comment "In mathematics, the Robin boundary condition (/ˈrɔːbɪn/; properly French: [ʁoˈbɛ̃]), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897).".
- Robin_boundary_condition label "Condición de frontera de Robin".
- Robin_boundary_condition label "Condition aux limites de Robin".
- Robin_boundary_condition label "Robin boundary condition".
- Robin_boundary_condition label "Третья краевая задача".
- Robin_boundary_condition label "ロビン境界条件".
- Robin_boundary_condition sameAs Condición_de_frontera_de_Robin.
- Robin_boundary_condition sameAs Condition_aux_limites_de_Robin.
- Robin_boundary_condition sameAs ロビン境界条件.
- Robin_boundary_condition sameAs m.02pxrtx.
- Robin_boundary_condition sameAs Q748993.
- Robin_boundary_condition sameAs Q748993.
- Robin_boundary_condition sameAs Robin_boundary_condition.
- Robin_boundary_condition wasDerivedFrom Robin_boundary_condition?oldid=580547643.
- Robin_boundary_condition isPrimaryTopicOf Robin_boundary_condition.