Consider crho ∂u ∂t = ∂ ∂x k0 ∂u ∂x ! + αu, where c, rho, k0 and α are functions of x, subject to u(0, t) = 0, u(l, t) = 0, u(x,0) = f (x). assume that appropriate eigenfunctions are known according to the results included in the box on p.157. (a) show that the eigenvalues are positive if α < 0. (b) solve the initial-boundary value problem. (c) discuss lim t→[infinity] u(x, t).