7.38 U, §2 PDE Model

• Finite domain :
• Unknown temperature
• Parabolic PDE:

  

• One homogeneous Neumann BC at r=a:

  

• One IC at t=0:

  

We will solve using separation of variables in the form

The eigenfunctions will get rid of the variable in the PDE, and the eigenfunctions R_nm will get rid of the r variable, leaving ODE for the Fourier coefficients u_nm(t).