EXERCISE (Instability). Consider the following initial value problem for u (t, x): Utt + uer = (x, y) ER2 (3.1) u (0, I) = TER ut (0, I) = sin nc TER where n E N is a positive integer. (1) Show that u (t, x) = (sinh nt ) (sin na) solves the initial value problem (3.1). (2) Show that by taking n sufficiently large, the absolute value of the initial data in (3.1) can be made arbitrarily small everywhere on the real line R, yet the solution can take arbitrarily large values even at points (t, r) with time t as small as we wish