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 presented as
The heat equation can also be presented as:


 * $\nabla^2 u = c^2\dfrac {\partial u} {\partial t}$

where $\nabla^2$ denotes the Laplacian of $u$.

Also known as
This equation is also known as the diffusion equation.

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

Also see

 * Solution to Heat Equation