Heat equation

From Citizendium
Revision as of 23:52, 2 September 2010 by imported>Gemma E. Mason (Began a basic description of what the equation is, what it is for, and how it may be solved.)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

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.