Given the equation ( uₜₜ - uₓₓ = 0 ), (x ∈ (-π, π)), (t ∈ [0, π]) with initial conditions ( u(x,0) = f(x) ), ( uₜ(x,0) = 0 ). We know that ( u(0,t) = g(t) ), ( uₓ(0,t) = h(t) ) where ( g ) and ( h ) are given on ( [0,π] ). For what ( T > 0 ) can you find ( f )?
a) (T = π)
b) (T = 2π)
c) (T = π/2)
d) (T = 0)
