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

TL;DR

This paper proves that coupling two well-posed evolution equations results in a new well-posed system, enabling analysis of complex models like predator-prey and epidemiological systems that were previously intractable.

Contribution

It establishes a general framework for the well-posedness of coupled differential models, including new classes of predator-prey and epidemiological systems.

Findings

Coupled systems generate a global process.

Application to predator-prey models.

Application to epidemiological models.

Abstract

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