Problem 1. Let u(t, x) be a bounded solution to the following problem for the heat equation Ut = Uxx, (t, x) = (0, t) x R u(0, x) = (x). Assume that the initial data p(x) = C(R) satisfies lim p(x) = b, X-X Compute the limit of u(t, x) as t , x R. lim p(x) = c. X118