Solving 2D Diffusion Problem: Analytical Solution Needed

[AndersFK]

I'm trying to find an analytical solution (probably containing a convolution integral) to a 2D diffusion problem in the xy-plane, when the value h(t) at the origin is known for all times t>=0. The diffusion constant is the same everywhere.

The last problem solved under the section http://en.wikipedia.org/wiki/Heat_equation#Homogeneous_heat_equation solves a similar problem for a semi-infinite 1D case. I've tried to expand their solution to the 2D case, but no luck so far.

Any comments/suggestions would be greatly appreciated.

 

[AndersFK]

I've found the solution. Carslaw & Jaeger (Conduction of Heat in Solids) solve the problem for $h(t)\equiv h_0$ constant. Duhamel's theorem can then be used to generalize the solution to the problem with a time-dependent boundary condition $h(t)$.