hello all.

does anyone know the general solution to the 2d heat equation, namely

$\displaystyle \frac{\partial u}{\partial \tau} = \frac{\partial^2 u}{\partial x_1^2} + \frac{\partial^2 u}{\partial x_2^2}$

subject to

$\displaystyle u(x_1,x_2,\tau = 0) = u_0(x_1,x_2)$

if anyone could help me I'd be well chuffed!