I'm supposed to solve for the concentration u(x,y,t) of a substance flowing into the following boundary:
The border is insulated so there is no flow out, same goes for the 4 blocks, and the red dot in the middle is the only source. I decided to split up the boundary into 21 subdomains, where the concentration of each subdomain is dependent on the other (therefore any side of a subdomain that touches the border or any block is essentially insulated). Am I approaching this the right way?
Also, time does not tend to infinity, it's bounded by a relatively small number, so the concentration will never become too great such that the boundary can't hold any more coming in.