ABSTRACT
E (x, t) = 1
2a ϑ ( at− |x|), ϑ(z) = {0 for z ≤ 0,
1 for z > 0. 3◦. Infinite series solutions containing arbitrary functions of the space variable:
w(x, t) = f(x) +
(2n)! f (2n)x (x), f
dxm f(x),
w(x, t) = tg(x) + t
(2n + 1)! g(2n)x (x),
where f(x) and g(x) are any infinitely differentiable functions. The first solution satisfies the initial conditions w(x, 0) = f(x) and ∂tw(x, 0) = 0, and the second w(x, 0) = 0 and ∂tw(x, 0) = g(x). The sums are finite if f(x) and g(x) are polynomials.
