Second-Order Linear Parabolic Equations

Abstract

Parabolic equations arise in diffusion processes, and more generally in “irreversible” time-dependent processes. Mathematically, this is reflected in the fact that the equations are not invariant under the reversal of time; i.e., under the transformation t → −t. This means that knowledge about the “past” is lost as time increases. For example, there may be dissipation effects which lead to an increase in entropy and a consequent loss of information.