A Partial Differential Equation of secondorder, i.e., one of the form

(1) 
is called parabolic if the Matrix

(2) 
satisfies det
. The Heat Conduction Equation and other
diffusion equations are examples. Initialboundary conditions are used to give

(3) 

(4) 
where

(5) 
holds in .
See also Elliptic Partial Differential Equation, Hyperbolic Partial Differential Equation,
Partial Differential Equation
© 19969 Eric W. Weisstein
19990526