
1214 BOUNDARY VALUE PROBLEMS. GREEN’S FUNCTION
By substituting the values set on the charac te ristics (17 .2.5.2) into the g eneral solution w =
ϕ(x −at) + ψ(x + at) of the wave equation, we arrive at a system of linear algebraic equations for
ϕ(x) and ψ(x). As a result, the solution of the Goursat problem is obtained in the form
w(x, t) = f
x + at
2
+ g
x − at
2
− f(0).
The solution pro pagation domain is the parallelogram bounded by the four lines
x − at = 0, x + at = 0, x − at = 2c, x + at = 2b.
⊙ Literature for Section 17.2: P. M. Morse and H. Feshbach (1953, Vol. 2), S. G. Mikhlin (1970), V. S . Vladi-
mirov (1971, 1988), S. J. Farlow (1982),