heat equation


The heat equation in 1-dimension (for example, along a metal wire) is a partial differential equationMathworldPlanetmath of the following form:

ut=c22ux2

also written as

ut=c2uxx

Where u:2 is the function giving the temperature at time t and position x and c is a real valued constant. This can be easily extended to 2 or 3 dimensions as

ut=c2(uxx+uyy)

and

ut=c2(uxx+uyy+uzz)

Note that in the steady state, that is when ut=0, we are left with the Laplacian of u:

Δu=0
Title heat equation
Canonical name HeatEquation
Date of creation 2013-03-22 12:45:36
Last modified on 2013-03-22 12:45:36
Owner drini (3)
Last modified by drini (3)
Numerical id 5
Author drini (3)
Entry type Definition
Classification msc 35Q99
Related topic DifferentialEquation
Related topic Laplacian