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- Biharmonic_equation abstract "In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear elasticity theory and the solution of Stokes flows. It is written asororwhere is the fourth power of the del operator and the square of the laplacian operator (or ), and it is known as the biharmonic operator or the bilaplacian operator. In summation notation, it can be written in dimensions as: For example, in three dimensional cartesian coordinates the biharmonic equation has the form As another example, in n-dimensional Euclidean space,wherewhich, for n=3 and n=5 only, becomes the biharmonic equation.A solution to the biharmonic equation is called a biharmonic function. Any harmonic function is biharmonic, but the converse is not always true.In two-dimensional polar coordinates, the biharmonic equation iswhich can be solved by separation of variables. The result is the Michell solution.".
- Biharmonic_equation wikiPageID "3010562".
- Biharmonic_equation wikiPageRevisionID "606365334".
- Biharmonic_equation hasPhotoCollection Biharmonic_equation.
- Biharmonic_equation title "Biharmonic Equation".
- Biharmonic_equation title "Biharmonic Operator".
- Biharmonic_equation urlname "BiharmonicEquation".
- Biharmonic_equation urlname "BiharmonicOperator".
- Biharmonic_equation subject Category:Elliptic_partial_differential_equations.
- Biharmonic_equation type Abstraction100002137.
- Biharmonic_equation type Communication100033020.
- Biharmonic_equation type DifferentialEquation106670521.
- Biharmonic_equation type EllipticPartialDifferentialEquations.
- Biharmonic_equation type Equation106669864.
- Biharmonic_equation type MathematicalStatement106732169.
- Biharmonic_equation type Message106598915.
- Biharmonic_equation type PartialDifferentialEquation106670866.
- Biharmonic_equation type Statement106722453.
- Biharmonic_equation comment "In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear elasticity theory and the solution of Stokes flows. It is written asororwhere is the fourth power of the del operator and the square of the laplacian operator (or ), and it is known as the biharmonic operator or the bilaplacian operator.".
- Biharmonic_equation label "Biharmonic equation".
- Biharmonic_equation label "Biharmonische Funktion".
- Biharmonic_equation label "Ecuación biarmónica".
- Biharmonic_equation label "Équation biharmonique".
- Biharmonic_equation label "Бигармоническая функция".
- Biharmonic_equation label "重調和方程式".
- Biharmonic_equation sameAs Biharmonische_Funktion.
- Biharmonic_equation sameAs Ecuación_biarmónica.
- Biharmonic_equation sameAs Équation_biharmonique.
- Biharmonic_equation sameAs 重調和方程式.
- Biharmonic_equation sameAs m.08kcpc.
- Biharmonic_equation sameAs Q859808.
- Biharmonic_equation sameAs Q859808.
- Biharmonic_equation sameAs Biharmonic_equation.
- Biharmonic_equation wasDerivedFrom Biharmonic_equation?oldid=606365334.
- Biharmonic_equation isPrimaryTopicOf Biharmonic_equation.