Show that the “backward” heat equation subject to u(0, t) = u(L, t) = 0 and u(x...

Show that the “backward” heat equation

subject to u(0, t) = u(L, t) = 0 and u(x, 0) = f(x), is not well posed. [Hint: Show that if the data are changed an arbitrarily small amount, for example,

for large n, then the solution u(x, t) changes by a large amount.]