ABSTRACT
Chapter 4
Green's Functions
for the Heat Equation
In this chapter, we present the Green's function
for the heat equa-
tion
@u
@t
a
r
u = q(r; t); (4:0:1)
where r is the three-dimensional gradient operator, t denotes time,
r is the position vector, a
is the diusivity, and q(r; t) is the source
density. In addition to (4.0.1), boundary conditions must be specied to
ensure the uniqueness of solution; the most common ones are Dirichlet,
Neumann and Robin (a linear combination of the rst two). An initial
condition u(r; t = t
) is also needed.
