H1 Prove the comparison principle for the diffusion equation: Let u and v be two C2 solutions of ut kua with k > 0 on [0, 1] [0, x). If u(x, t) < v(x, t) for (x, t) E [0,1] {0}, for (x, t) E {0} [0, 0) and for (x, t) E {l} [0, 0), then u