(1) u( ath, t + k) tu(x - h,t - k) = u(r + k, t + h) tu(r - k, t -h), for any r, t, k, he R. What is the geometrical meaning of (1). - 2) Consider the initial boundary value problems: OFu - O2u = 0, I E (0, T), t> 0, u(x, 0) = 0, du(r, 0) =1, re (0, 7), initial data, u(0, t) = 0, w ( IT, t ) = 0, t >0, boundary values. (a) Solve it using formula (1). (b) Is the resulting solution continuous? Is C' i.e, u(r, t) differentiable with du(x, t), dru(c, t) continuous