Solving the inhomogeneous two dimensional heat equation

125 Views Asked by Bumbble Comm At 25 Mar 2026 - 9:46

I am currently interested in solving the inhomogeneous heat equation for a two dimensional flow for a bounded domain. The PDE is given as:

I was thinking about solving this by using the Fundamental solution as:

with

However since the inhomogeneous function is given as a rather "complicated" structure in terms of integration, I struggle quiete a lot there.

Do you have any ideas or experience in how to solve suche an inhomogeneous heat equation?

I would also appreciate any guidance in how to solve the inhomogeneous heat equation in genereal for a two dimensional flow.

I am very thankful for any advice