
5.2. Heat Equation with Source
∂w
∂t
= a∆
3
w + Φ(x, y, z, t) 533
2
◦
. The solution w(r, ϕ, z, t) of the second boundary value problem for an infinite wedge
domain is given by the formula in Section 5.1.2 (see the second boundary value problem
for 0 ≤ r < ∞, 0 ≤ ϕ ≤ ϕ
0
, −∞ < z < ∞) with the additional term (6); the Green’s
function is also taken from Section 5.1.2.
◮ Domain: 0 ≤ r < ∞, 0 ≤ ϕ ≤ ϕ
0
, 0 ≤ z < ∞. Different boundary value
problems.
1
◦
. The solution w(r, ϕ, z, t) of the first boundary value problem for a semiinfinite wedge
domain is given by the formula in S ection 5.1.2 (see the first boundary value problem for
0 ≤ r < ∞, 0 ≤ ϕ ≤ ϕ
0
, 0 ≤ z < ∞) with ...