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conservation condition for rate equations (PDE)

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I'm trying to model a structure with the RF module (time dependent) coupled with a system of differential equations that describes the rate equations of atoms populations in different energy levels (similar to the rate equations of a laser).

it's a 4 energy levels system (4 populations to be computed with time N0...N3) so I've 4 eq. diff defined through the Coefficient form PDE interface. I'm now facing difficulties in adding a conservation equation that states that at any given time the total population in the whole system remains equal to the initial population of the ground energy level (N0+....+N4=N0_t0).

Can you tell where I could add such a conservation equation. It's important to emphasize that this conservation is at any time and over all the simulation domain where the system is defined.

I'm looking forward for your help.

Best Regards,

Michael

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