ABSTRACT
In this chapter, we present the Green’s function1 for the heat equation
∂u
∂t − a2∇2u = q(r, t), (5.0.1)
where ∇ is the three-dimensional gradient operator, t denotes time, r is the position vector, a2 is the diffusivity, and q(r, t) is the source density. In addition to Equation 5.0.1, boundary conditions must be specified to ensure the uniqueness of solution; the most common ones are Dirichlet, Neumann and Robin (a linear combination of the first two). An initial condition u(r, t = t0) is also needed.
