# Definition:Heat Equation

## Equation

The heat equation is a second order PDE of the form:

$a^2 \paren {\dfrac {\partial^2 w} {\partial x^2} + \dfrac {\partial^2 w} {\partial y^2} + \dfrac {\partial^2 w} {\partial z^2} } = \dfrac {\partial w} {\partial t}$

## Also known as

Some sources refer to this equation as Fourier's equation, for Joseph Fourier, but while the attribution is clear, this usage is rare.