I need to solve this heat equation:
$\left\{ \begin{gathered} \frac{{\partial u}}{{\partial t}} = A\Delta U,|\overrightarrow x | < R,t > 0 \hfill \\ - \alpha \frac{{\partial u}}{{\partial \overrightarrow n }} = \beta (u - {u_0}),|\overrightarrow x | = R,t > 0 \hfill \\ u(x,0) = {u_h},|\overrightarrow x | < R \hfill \\ \end{gathered} \right.$
where $\overrightarrow n$ is the outer normal of the ball $|\overrightarrow x|<R$. Could anyone give some hint on solving this kind of boundary value problem? Thanks!