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