
720 SECOND-ORDER HYPERBOLIC EQUATIONS WITH THREE OR MORE SPA CE VARIABLES
3
◦
. The solution w(r, θ, ϕ, t) of the third boundary value problem for a sphere is the sum of
the solution specified in Section 8.1.3 (see the third boundary value problem for 0 ≤ r ≤R,
0 ≤ θ ≤ π, 0 ≤ ϕ ≤ 2π) and expression (1); the Green’s function is also taken from
Section 8.1.3.
◮ Domain: R
1
≤ r ≤ R
2
, 0 ≤ θ ≤ π, 0 ≤ ϕ ≤ 2π. Boundary value problems.
1
◦
. The solution w(r, θ, ϕ, t) of the first boundary value problem for a spherical layer is
given by the formula from Section 8.1.3 (see the first boundary value problem for R
1
≤
r ≤ R
2
, 0 ≤ θ ≤ π, 0 ≤ ϕ ≤ 2π) with the additional term ...