
446 SECOND-ORDER PARABOLIC EQUATIONS WITH TWO SPACE VARIABLES
Here,
G(r, z, ξ, η, t) = G
1
(r, ξ, t) G
2
(z, η, t),
G
1
(r, ξ, t) =
1
πR
2
∞
X
n=1
1
J
2
1
(µ
n
)
J
0
µ
n
r
R
J
0
µ
n
ξ
R
exp
−
aµ
2
n
t
R
2
,
G
2
(z, η, t) =
1
2
√
πat
exp
−
(z − η)
2
4at
− exp
−
(z + η)
2
4at
,
where the µ
n
are positive zeros of the Bessel function, J
0
(µ
n
) = 0. The numerical values
of the first ten µ
n
are specified in Section 3.2.1 (see the first boundary value problem for
0 ≤ r ≤ R).
⊙ Literature: H. S. Carslaw and J. C. Jaeger (1984).
◮ Domain: 0 ≤ r ≤ R, 0 ≤ z < ∞. Second b oundary value problem.
A semiinfinite circular cylinder is considered. The following conditions are prescribed:
w = f (r, z) at t = 0 (initial condition ...