
658 SECOND-ORDER HYPERBOLIC EQUATIONS WITH TWO SPACE VARIABLES
2
◦
. A circular cylinder of finite length is considered. The following conditions are pre-
scribed:
w = f
0
(r, z) at t = 0 (initial condition),
∂
t
w = f
1
(r, z) at t = 0 (initial condition),
∂
r
w = g
1
(z, t) at r = R (boundary condition),
w = g
2
(r, t) at z = 0 (boundary condition),
w = g
3
(r, t) at z = l (boundary condition).
The solution w(r, z, t) is given by the formula in Section 7.1.3 (see Item 2
◦
for the
mixed boundary value problems for 0 ≤ r ≤ R, 0 ≤ z ≤ l) with the additional term (1);
the Green’s function is also taken from S ection 7.1.3.
◮ Domain: R
1
≤ r ≤ R
2
, 0 ≤ z ≤ l. First boundary