
7.2. Nonhomogeneous Wave Equation
∂
2
w
∂t
2
= a
2
∆
2
w + Φ(x, y, t) 653
The solution w(x, y, t) is given by the formula in Section 7.1.1 (see the third boundary
value problem for 0 ≤ x ≤l
1
, 0 ≤ y ≤l
2
) with the additional term (1); the Green’s function
is also taken from Section 7.1.1.
⊙ Literature: A. G. Butkovskiy (1979), B. M. Budak, A. A. Samarskii, and A. N. Tikhonov (1980).
◮ Domain: 0 ≤ x ≤ l
1
, 0 ≤ y ≤ l
2
. Mixed boundary value problems.
1
◦
. A rectangle is considered. The following conditions are prescribed:
w = f
1
(x, y) at t = 0 (initial condition),
∂
t
w = f
2
(x, y) at t = 0 (initial condition),
w = g
1
(y, t) at x = 0 (boundary condition),
w = g
2
(y, t) at ...