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 see

 * Solution to Heat Equation