Boundary Values & Fourier Series · Medium problem

A rod $0 \le x \le 3$ with both ends insulated ($u_x(0,t) = u_x(3,t) = 0$) obeys $u_t = u_{xx}$ and starts at $u(x, 0) = x^2$. Find $\displaystyle\lim_{t\to\infty} u(x, t)$.