3. Consider the heat equation in a two-dimensional rectangular region O co, if the boundary conditions are a. u(0, y, t) = 0, u(L, y, t) =0, u(x, 0, t) = 0, u(x, H, t) = 0. b. ax (0, y, t) = 0, " ( L, y, t) = 0, dy (2, 0,t) = 0, ' a (* , H, t) = 0. Note: You may assume without derivation that product solutions u(x, y, t) = (x, y)h(t) = f(x)g(y)h(t) satisfy dh dt =-Akh, and the two-dimensional eigenvalue problem V2 + A = 0 with further separation d2 f dac2 = -uf , d'g dy2 + (1 - 1)g = 0, or you may use results of the two-dimensional eigenvalue