Comparison principle. Show the following comparison principle. If u and v are two solutions of ut = uxx + f(x, t)
on (0, l) ⇥ (0, 1) and if u(x, 0)  v(x, 0) in [0, l] and u(0, t)  v(0, t) and u(l, t)  v(l, t) for
t > 0, then u(x, t)  x(x, t) on (0, l) ⇥ (0, 1).

Comparison principle
Show the following comparison principle. If u and v are two solutions of ut = uxx + f(x, t)
on (0, l) ⇥ (0, 1) and if u(x, 0)  v(x, 0) in [0, l] and u(0, t)  v(0, t) and u(l, t)  v(l, t) for
t > 0, then u(x, t)  x(x, t) on (0, l) ⇥ (0, 1).