Trying to find the Green's function of a PDE

[ptrinka]

Dear all,

I am trying to find the Green's function of the following PDE:

\(\displaystyle \frac{\partial{u}}{\partial t}=A\cdot \nabla^2{u}-B\cdot u\)

I.C.
\(\displaystyle u(x,y,0)=0\)

Note that A and B are constants.

Any hint?

Thanks!