Biharmonic equation

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 as

or

where $\nabla^4$ is the fourth power of the del operator and the square of the laplacian operator $\nabla^2$ (or $\Delta$ ), and it is known as the biharmonic operator or the bilaplacian operator. In summation notation, it can be written in $n$ dimensions as:

单词	Biharmonic equation
释义	Biharmonic equation 英语例句库 According to the nature of two-dimensional biharmonic equations,this paper obtains a polynomial solution of the biharmonic equation for stress function by means of the MATHEMATICA software. 根据二维双调和方程的特点并借助于MATHEMATICA软件,得到了应力函数双调和方程的多项式解答。英语百科 Biharmonic equation 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 as or or where $\nabla^4$ is the fourth power of the del operator and the square of the laplacian operator $\nabla^2$ (or $\Delta$ ), and it is known as the biharmonic operator or the bilaplacian operator. In summation notation, it can be written in $n$ dimensions as:
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