Heat equation

From Citizendium
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
This editable Main Article is under development and subject to a disclaimer.

The heat equation is a partial differential equation of the form

where denotes the Laplacian. When there is only one spatial dimension being considered, the heat equation takes the form

The heat equation is so called because it was studied by Joseph Fourier as a way of describing the way heat spreads over time. The heat equation can also be used to describe other processes such as diffusion.

On an infinite spatial domain, the heat equation is usually solved using the Fourier transform. On a finite spatial domain, separation of variables is often used along with the Fourier series.