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I have a PDE of the form

f(x,y,z)'' = Δf(x,y,z) + f(x,y,z) * (1 - f(x,y,z)^2)

where f(x,y,z) is a 3 dimensional vector-field.

Now I want to compute an energy function for it such that for any state (f(x,y,z) and its first derivative f(x,y,z)') I can compute its corresponding energy (which should stay constant over the whole domain during evolution of the system, but may vary for parts of it).

How would I do this ? Can someone help me out here ?

Thanks and cheers

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# How to compute an energy function of PDE ?

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