How to Integrate Solved Values in a 2D Domain？

General
1

Hi all, I am currently solving a diffusion model and the process has been very successful. When using the 1D model before, to integrate over the domain for concentration c, I used the following:
total = assemble(c*dx)
But now that I’ve become a 2D domain, I want the concentration c to be area partitioned over the domain, how do I accomplish this?

2

Without a minimal example at hand it is quite hard to decipher what you want to do.
Do you:

  1. Given a know total concentration T distribute this over a 2D domain?
  2. Do you want to compute the total concentration T from a known (or derived density c)?
3

I want to solve this equation：
1710344487914(1)
where c is the concentration (/m^3)

4

Where c is known? What is wrong with doing assemble(c*dx(domain=mesh)), if your mesh is the 2D domain you want to integrate over?

5

Thank you. I get it.