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Consider the coupling of $2$ evolution equations, each generating a globalprocess. We prove that the resulting system generates a new global process.This statement can be applied to differential equations of various kinds. Inparticular, it also yields the well posedness of a predator-prey model, wherethe coupling is in the differential terms, and of an epidemiological model,which does not fit previous well posedness results.

On the Coupling of Well Posed Differential Models -- Detailed Version