4. If u and v are two solutions of the heat equation and if u(x, 0) v(x, 0), and u(0, t) v(0, t), and u(L,t) v(L, t), show that u(x, t) v(x, t) for all 0 < x 0. 5. Prove the uniqueness of the diffusion problem with Neumann boundary conditions: using the energy method. utkuxx 0