Please find the solution for u(t, r) for 0 < r < a and 0 < t < 2T, with t = [0, T]. The boundary and initial conditions will be of the form u(r, 0, 0) = f(r, 0), u_t(r, 0, 0) = F(r, 0), u(a, 0, t) = 0, for all 0 on the (circular) boundary. Let a = 10 and c = 1/2 with f(r, 0) = sin(20) and F(r, 0) = 0, over a suitable time interval t = [0, up to you].
