Two dimensional heat equation with source

  • #1
I have the following PDE

PDE: ut=A2(uxx+uyy)+f(x,y,t) such that A is a constant
BC: ux(1,y,t)=0
ux(0,y,t)=0
uy(x,1,t)=0
u(x,0,t)=0
IC: u(x,y,0)=0

I've set up my ODEs using seperation of variables to get

X''/X=k1 Y''/Y=k2 T'/(A2)T=k1+k2

where k1 and k2 are constants.



How do I account for my source term (f(x,y,t))? I'm reading up on eigenfunction expansion but so far it's only for the dimensional case.
 
Last edited:

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