Biharmonic equation

A mathematical function is called biharmonisch in an area, if the so-called biharmonic equation

Satisfied for all points. here is the Laplace operator. The biharmonic equation is thus a partial differential equation of fourth order.

In practice, this equation occurs in the continuum mechanics in drives for example. The deformation of a disk in a first approximation point obeys the inhomogeneous biharmonic equation:

Here, the force ( density) applied to the plate.

Harmonic functions are always biharmonic functions; but the converse does not apply.