So, by working out a physics equation, I ended up with Poisson's equation: $$ \nabla^2A=G. $$ Now the thing is, $A$ is not some sort of potential, but a physical quantity, energy in my case. If the Laplacian operator essentially gives you the curvature of the quantity $A$, so that if it is negative at a specific point for example, it's value there is greater than that of the surrounding points, then could we consider $G$ as a "source" term if it is negative, and a "sink" if it is positive? I know for the electric potential for example, a distribution of charges is a source for the electric field, which is the negative of the gradient of the potential. But what about when the quantity under the Laplacian is the more meaningful quantity?
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Since you know that A is energy in your case, and that the same equation can apply to other quantities, what more can we tell you about it? – D. Halsey Feb 05 '22 at 15:16
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Well, am I supposing right or wrong in seeing $G$ as a source or sink for $A$, even if it is not a time evolution equation? – BitterDecoction Feb 05 '22 at 16:08