Given an infinitely long cylinder with radius a, we want to model the diffusive transport of molecules represented by u(r,t) to the wall, where r is the radial component. Given $$ \frac{\partial u}{\partial t} = D \frac{\partial^2 u}{\partial r^2} $$ where $D$ is the diffusion constant. Initial/boundary conditions are $u(r,0)=u_0>1$ and $u(a,t)=1$.
Find $u(r,t)$ using fourier transforms.
I was given the hint to find the steady state solution first and then subtract it from the full solution to solve with fourier transforms for homogeneous boundary conditions, but I'm stuck.