I have this particular instance of the Heat Equation: Find u such that
$$\label{eq:Neumann_parabolico} \left\lbrace \begin{array}{rl} u_t + \Delta u = 0 & \mbox{in } B(0,1)\times (0,T], \\ u = 0 & \mbox{in } \partial B(0,1) \times (0,T],\\ u(\cdot,0) = \delta_0 & \mbox{in } B(0,1), \end{array} \right. $$ for some final $T>0$. Here $B(0,1) \subset \mathbb{R}^2$ is the unitary ball centered at 0, and $\delta_0$ is the Dirac delta function.
My question: Is there a closed-form expression for the solution $u(x,y,t)$?
I tried to use the fact that $u$ should have radial symetry, but I didn't succeed...