I'm trying to understand what I need to do to get Maple to solve the heat equation in spherical coordinates. I'm considering a test problem: a spherical shell with inner radius 1 and outer radius 2. Boundary conditions require the temperature of the inner and outer surfaces are to always equal zero. The initial condition requires the temperature inside the shell to be -sin(pi*r).
The attached worksheet provides my attempt to solve this problem. Executing this worksheet will quickly give a general solution but this does not include the initial condition. If this is included then Maple fails to give a solution even after a 20 min wait.
Could someone offer me guidance on how to proceed?