
488 SECOND-ORDER PARABOLIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES
◮ Remarks on the Green’s functions.
For the three-dimensional problems dealt with in Section 5.1.2, the Green’s function can
be represented in the product form
G(r, ϕ, z, ξ, η, ζ, t) = G
1
(r, ϕ, ξ, η, t) G
2
(z, ζ, t),
where G
1
(r, ϕ, ξ, η, t) is the Green’s function of the two-dimensional boundary value prob-
lem (such functions are presented in Section 4.1.2), and G
2
(z, ζ, t) is the Green’s func-
tion of the corresponding one-dimensional boundary value problem (such functions can be
found in Sections 3.1.1 and 3.1.2).
Example 5.5. The Green’s function of the first boundary value problem ...